Frigon, Marlène
- Full Professor
-
Faculty of Arts and Science - Department of Mathematics and Statistics
André-Aisenstadt Office 5143
Courriels
Affiliations
- Membre Centre de recherches mathématiques
- Membre CRM Centre de recherches mathématiques
Courses
- MAT2050 A - Analyse 2
Research area
Student supervision Expand all Collapse all
Théorèmes d’existence pour des équations différentielles de Stieltjes à l’aide des g-régions-solutions
Theses and supervised dissertations / 2023-12
Mayrand, Julien
Abstract
Abstract
The method of solution-regions has been developed by Frigon [7] in 2018 to show the existence of solutions for first-order ordinary differential equations, where the graph of a solution is inside a solution-region \(R \subset [0, T] \times \mathbb{R}^{N}\). This method is in particular a generalization of the lower and upper solutions and of the solution-tubes. We show this method and some existence results which follow.
On the other hand, the Stieltjes derivative, more commonly called \(g\)-derivative, is the fruit of the work of Pouso and Rodríguez [20] in 2014, which unifies classic differential equations, equations on time scales and differential equations with impulses. In particular, it leads to the fundamental theorem of calculus for the Lebesgue-Stieltjes integral. We start by showing the basis of this theory, and then the way this \(g\)-derivative generalizes other types of differential or time scale equations. We introduce in particular the \((g \times I_{\mathbb{R}^{N}})\)-differentiability and results that follow from this definition. Furthermore, we present an exponential function which solves linear Stieltjes differential equations.
The goal of this thesis is to generalize the method of solution-regions, where the generalization will be called \(g\)-solution-region, to show the existence of solutions for Stieltjes differential equations. We present multiple examples of \(g\)-admissible regions and \(g\)-solution-regions, then we establish existence theorems based on this method. We also show examples where we apply these theorems.
Finally, we end this thesis by showing two applications of the existence theorems to the evolution of a population of white-tailed deer and to the evolution of the voltage generated by a resonant tunneling diode (RTD) to a laser diode (LD).
Sur les solutions d'équations différentielles de Stieltjes du
premier et du deuxième ordre
Theses and supervised dissertations / 2018-10
Larivière, François
Abstract
Abstract
The Stieltjes derivative, or g-derivative, was introduced by Pouso and RodrÍguez to obtain an equivalent of the fundamental theorem of calculus for the Lebesgue-Stieltjes integral. This derivative also allows the generalization of different types of differential equations. This thesis introduces the g-derivative and exposes work done until now in the demonstration of generalizations of results known for differential equations; namely the definition of an exponential function as the solution of a first order linear homogeneous equation and existence and uniqueness results for first-order systems of Stieljtes differential equations. We proceed by generalizing some results, for example the existence of a maximal interval of existence for solutions and the continuous dependence on initial conditions. We introduce the second order linear equation and present results on the existence and uniqueness of solutions, as well as their form. These equations allow us to introduce equivalents of the trigonometric and hyperbolic functions. Finally, we emphasize the pertinence of this new derivative, by showing how it generalizes previous attempts at unifying discrete and continuous calculus and by applying the theory of Stieltjes differential equations to the modeling of a population of drosophilae.
Fixed point results for multivalued contractions on graphs and their applications
Theses and supervised dissertations / 2015-06
Dinevari, Toktam
Abstract
Abstract
In this thesis, we present fixed point theorems for multivalued contractions defined
on metric spaces, and, on gauge spaces endowed with directed graphs. We also
illustrate the applications of these results to integral inclusions and to the theory
of fractals. chapters. In Chapter 1, we establish fixed point results for the maps, called multivalued
weak G-contractions, which send connected points to connected points
and contract the length of paths. The fixed point sets are studied. The homotopical
invariance property of having a fixed point is also established for a
family of weak G-contractions. In Chapter 2, we establish the existence of solutions
of systems of Hammerstein integral inclusions under mixed monotonicity
type conditions. Existence of solutions to systems of differential inclusions with
initial value condition or periodic boundary value condition are also obtained.
Our results rely on our fixed point theorems for multivalued weak G-contractions
established in Chapter 1. In Chapter 3, those fixed point results for multivalued
G-contractions are applied to graph-directed iterated function systems. More
precisely, we construct a suitable metric space endowed with a graph G and an
appropriate G-contraction. Using the fixed points of this G-contraction, we obtain
more information on the attractors of graph-directed iterated function systems. In Chapter 4, we consider multivalued maps defined on a complete gauge space
endowed with a directed graph. We establish a fixed point result for maps which
send connected points into connected points and satisfy a generalized contraction
condition. Then, we study infinite graph-directed iterated function systems
(H-IIFS). We give conditions insuring the existence of a unique attractor to an
H-IIFS. Finally, we apply our fixed point result for multivalued contractions on
gauge spaces endowed with a graph to obtain more information on the attractor
of an H-IIFS. More precisely, we construct a suitable gauge space endowed with
a graph G and a suitable multivalued G-contraction such that its fixed points are
sub-attractors of the H-IIFS.
Théorèmes de point fixe et principe variationnel d'Ekeland
Theses and supervised dissertations / 2010-02
Dazé, Caroline
Abstract
Abstract
The Banach contraction principle, which certifies that a contraction of a complete metric space into itself has a fixed point, is for sure the most famous of all fixed point theorems. However, in many case, the contraction we consider is only defined on a subset of a complete metric space. Of course, to certify that such a contraction has a fixed point, we need to add some restrictions. The Caristi theorem, which certifies the existence of a fixed point of a function of a complete metric space into itself satisfying a particular condition on d(x,f(x)), was later generalized to multivalued functions. By introducing different types of inwardness assumptions, we will be able to state some fixed point theorems for multivalued functions defined on a subset of a metric space. This is related to the recent work of French and Polish mathematicians. We were able to generalize some theorems to Fréchet spaces and gauge spaces such as the Caristi theorems and the Ekeland variational principle. We were also able to generalize some fixed point theorems for functions that are only defined on a subset of a Fréchet space or a gauge space. To do so, we used new types of contractions; contractions on Fréchet spaces introduced by Cain and Nashed [CaNa] in 1971 and generalized contractions on gauge spaces introduced by Frigon [Fr] in 2000.
Quelques théorèmes de points critiques basés sur une nouvelle notion d'enlacement
Theses and supervised dissertations / 2009-12
Boulanger, Laurence
Abstract
Abstract
A new notion of linking for pairs of sets $A\subset B$, $P\subset Q$ in a Hilbert space of the form $X=Y\oplus Y^{\perp}$ with $Y$ separable, called $\tau$-linking, is defined. The model for this definition is the generalization of homotopical linking and linking in the sense of Benci-Rabinowitz made by Frigon. Using the degree theory developped in an article of Kryszewski and Szulkin, many examples of $\tau$-linking pairs are given. A deformation lemma is established and used jointly with the notion of $\tau$-linking to prove an existence theorem for critical points of a certain class of functionals defined on $X$. Moreover, a characterization of a minimax nature for the corresponding critical value is given. As a corollary of this theorem, conditions are stated under which the existence of two distinct critical points is guaranteed. Two other critical point theorems are demonstrated, one of which generalizes the main theorem of the article of A new notion of linking for pairs of sets $A\subset B$, $P\subset Q$ in a Hilbert space of the form $X=Y\oplus Y^{\perp}$ with $Y$ separable, called $\tau$-linking, is defined. The model for this definition is the generalization of homotopical linking and linking in the sense of Benci-Rabinowitz made by Frigon~\cite{frigon:1}. Using the degree theory developped in~\cite{szulkin:1}, many examples of $\tau$-linking pairs are given. A deformation lemma is established and used jointly with the notion of $\tau$-linking to prove an existence theorem for critical points of a certain class of functionals defined on $X$. Moreover, a characterization of a minimax nature for the corresponding critical value is given. As a corollary of this theorem, conditions are stated under which the existence of two distinct critical points is guaranteed. Two other critical point theorems are demonstrated, one of which generalizes the main theorem of the article by Kryszewski and Szulkin cited above.
Théorèmes d'existence pour des systèmes d'équations différentielles et d'équations aux échelles de temps
Theses and supervised dissertations / 2009-10
Gilbert, Hugues
Abstract
Abstract
In this thesis, we present existence theorems for systems of third order nonli-
near differential equations, for systems of first order nonlinear time scales equa-
tions and inclusions and for systems of second order nonlinear time scales equa-
tions under some boundary conditions. In chapter three, we introduce a concept
of solution-tube to get existence theorems for systems of third order differential
equations. This new definition generalizes to systems the notions of lower- and
upper-solution to third order differential equations introduced in [34]. In the last
part of this chapter, we study third order systems when the right member f sa-
tisfies a Wintner-Nagumo growth condition. To obtain an existence result in this
case, we use the theory of differential inclusions. This result generalizes in many
ways a theorem due to Grossinho and Minhós [34].
The next chapter concerns the existence of solutions for two kind of systems of
first order time scales equations. Existence results for these problems are obtained
with new notions of solution-tube adapted to these systems. Our first theorem ge-
neralizes to systems and to an arbitrary time scale a result for difference equations
due to Mawhin and Bereanu [9]. Our result permits to deduce the existence of so-
lutions for systems which could not be treated in a result of Dai and Tisdell [17].
The second theorem of this chapter generalizes under few conditions some results
of [60]. The fifth chapter presents a new existence theorem for a system of first
order time scales inclusions. As far as we know, there is no result in the littera-
ture for this kind of system of inclusions. Therefore, this chapter opens new doors
in the branch of time scales inclusions. Again, our new result is obtained with
the introduction of an hypothesis of solution-tube adapted to the problem studied.
In the last chapter, existence of solutions for systems of second order time
scales equations are obtained. The first result of this chapter generalizes theo-
rems of [36] since the hypothesis used by these authors to get a priori bounds
for solutions is a particular case of our definition of solution-tube for this type
of problems. Let us mention also that our notion of solution-tube generalizes to
systems the definitions of lower- and upper-solution used for second order time
scales equations by [4] and [55]. We also generalize to systems, results obtained
for second order time scales equations. Finally, we conclude this chapter with a
new existence result for systems of second order time scales equations with a right
member depending on the ∆-derivative.
Dégénérescence et problèmes extrémaux pour les valeurs propres du laplacien sur les surfaces
Theses and supervised dissertations / 2008
Girouard, Alexandre
Abstract
Abstract
Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal.
Catégorie assujettie à une fonctionnelle et une application aux systèmes Hamiltoniens
Theses and supervised dissertations / 2006
Beauchemin, Nicolas
Abstract
Abstract
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.
Chirurgie de Dehn et la conjecture propriété P
Theses and supervised dissertations / 2005
Ayotte-Sauvé, Étienne
Abstract
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
Quelques résultats d'existence de points asymptotiquement critiques
Theses and supervised dissertations / 2004
Perreault, Jean-François
Abstract
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
Existence et multiplicité de solutions de systèmes d'équations et de systèmes d'inclusions différentielles avec opérateurs maximaux monotones
Theses and supervised dissertations / 2004
Montoki, Emmanuel
Abstract
Abstract
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.
Enlacement homologique relatif
Theses and supervised dissertations / 2002
Girouard, Alexandre
Abstract
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
Théorie des points critiques pour une fonctionnelle multivoque invariante
Theses and supervised dissertations / 1999
Beauchemin, Nicolas
Abstract
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
Généralisation de résultats sur l'enlacement local en théorie des points critiques
Theses and supervised dissertations / 1999
Picard, Frédéric
Abstract
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
L'indice de Conley
Theses and supervised dissertations / 1999
Santerre, Julie
Abstract
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
Résultats d'existence pour des systèmes d'équations différentielles du premier ordre avec tube-solution
Theses and supervised dissertations / 1996
Mirandette, Benoit
Abstract
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
Existence et multiplicité de solutions d'équations différentielles non linéaires et non continues
Theses and supervised dissertations / 1995
Goudreau, Kim
Abstract
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.
Research projects Expand all Collapse all
Centre de recherches mathématiques (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2022 - 2029
CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2015 - 2023
THEORIES DES POINTS FIXES ET DES POINTS CRITIQUES EN ANALYSE NON LINEAIRE ET APPLICATIONS CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2013 - 2022
CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2008 - 2016
METHODES VARIATIONNELLES ET TOPOLOGIQUES EN ANALYSE NON LINERAIRE / 2008 - 2012
Selected publications Expand all Collapse all
Multiplicity results for systems of first order dynamic inclusions on time scales
M. Frigon, M. Lotfipour, Multiplicity results for systems of first order dynamic inclusions on time scales , (2015), , Applied Math. Computation
A contraction principle on gauge spaces with graphs and application to infinite graph-directed iterated function systems
T. Dinevari, M. Frigon, A contraction principle on gauge spaces with graphs and application to infinite graph-directed iterated function systems , (2015), , Fixed Point Theory
Systems of Hammerstein integral inclusions in Banach spaces with mixed monotone conditions
T. Dinevari, M. Frigon, Systems of Hammerstein integral inclusions in Banach spaces with mixed monotone conditions , (2015), , J. Inequalities Appl.
Applications of multivalued contractions on graphs to graph-directed iterated function systems
T. Dinevari, M. Frigon, Applications of multivalued contractions on graphs to graph-directed iterated function systems 2015, 16 (2015), , Abstr. Appl. Anal.
Multiple solutions of problems with nonlinear first order differential operators
N. El Khattabi, M. Frigon, N. Ayyadi, Multiple solutions of problems with nonlinear first order differential operators , (2015), , J. Fixed Point Theory Appl.
Multiplicity results for systems of first order differential inclusions
M. Frigon, M. Lotfipour, Multiplicity results for systems of first order differential inclusions 16, 1025-1040 (2015), , J. Nonlinear Convex Anal., Special issue entitled ``Nonlinear Functional Analysis'' dedicated to the memory Professor Francesco S. de Blasi
Fixed point results for multivalued contractions on a metric space with a graph
T. Dinevari, M. Frigon, Fixed point results for multivalued contractions on a metric space with a graph 405, 507--517 (2013), , J. Math. Anal. Appl.
Multiple solutions of boundary value problems with $\phi$-Laplacian operators and under a Wintner-Nagumo growth condition
N. El Khattabi, M. Frigon, N. Ayyadi, Multiple solutions of boundary value problems with $\phi$-Laplacian operators and under a Wintner-Nagumo growth condition 2013, 21 (2013), , Bound. Value Probl.
On some generalizations of Ekeland's principle and inward contractions in gauge spaces
M. Frigon, On some generalizations of Ekeland's principle and inward contractions in gauge spaces 10, 279--298 (2011), , J. Fixed Point Theory Appl.
Systems of first order inclusions on time scales
M. Frigon, H. Gilbert, Systems of first order inclusions on time scales 37, 147--163 (2011), , Topol. Methods Nonlinear Anal.
Boundary value problems for systems of second-order dynamic equations on time scales with $delta$-Carathéodory functions
M. Frigon, H. Gilbert, Boundary value problems for systems of second-order dynamic equations on time scales with $delta$-Carathéodory functions Frigon, M. and Gilbert, H., Art. ID 234015, 26 (2010), , Abstr. Appl. Anal.
Existence theorems for systems of third order differential equations
M. Frigon, H. Gilbert, Existence theorems for systems of third order differential equations 19, 1--23 (2010), , Dynam. Systems Appl.
Fixed point results for multivalued maps in metric spaces with generalized inwardness conditions
M. Frigon, Fixed point results for multivalued maps in metric spaces with generalized inwardness conditions Frigon, M., Art. ID 183217, 19 (2010), , Fixed Point Theory Appl.
On a notion of category depending on a functional. II. An application to Hamiltonian systems
N. Beauchemin, M. Frigon, On a notion of category depending on a functional. II. An application to Hamiltonian systems 72, 3376--3387 (2010), , Nonlinear Anal.
On a notion of category depending on a functional. I. Theory and application to critical point theory
N. Beauchemin, M. Frigon, On a notion of category depending on a functional. I. Theory and application to critical point theory 72, 3356--3375 (2010), , Nonlinear Anal.
Multiplicity results for systems of second order differential equations
M. Frigon, E. Montoki, Multiplicity results for systems of second order differential equations 15, 71--92 (2008), , Nonlinear Stud.
Systems of first order differential inclusions with maximal monotone terms
M. Frigon, Systems of first order differential inclusions with maximal monotone terms 66, 2064--2077 (2007), , Nonlinear Anal.
Fixed point and continuation results for contractions in metric and in gauge spaces
M. Frigon, Fixed point and continuation results for contractions in metric and in gauge spaces 77, 89--114 (2007), , Fixed Point Theory and its Applications, Banach Center Publ., Polish Acad. Sci., Warzaw
Global existence of analytic solutions to the Cauchy problem in a complex domain
M. Frigon, Global existence of analytic solutions to the Cauchy problem in a complex domain 1, 189--194 (2007), , J. Fixed Point Theory Appl.
Systems of coupled Poisson equations with critical growth in unbounded domains
F. Colin, M. Frigon, Systems of coupled Poisson equations with critical growth in unbounded domains 13, 369--384 (2006), , NoDEA Nonlinear Differential Equations Appl.
Systems of differential inclusions with maximal monotone terms
M. Frigon, E. Montoki, Systems of differential inclusions with maximal monotone terms 323, 1134--1151 (2006), , J. Math. Anal. Appl.
Systems of singular Poisson equations in unbounded domains
F. Colin, M. Frigon, Systems of singular Poisson equations in unbounded domains CRM-3177, 18 (2005), , Rapport de recherche, CRM, Université de Montréal
Systems of singular Poisson equations in unbounded domains
F. Colin, M. Frigon, Systems of singular Poisson equations in unbounded domains 10, 1035--1052 (2005), , Adv. Differential Equations
A note on upper and lower solutions for first order inclusions of upper semicontinuous or lower semicontinuous type
R.P. Agarwal, M. Frigon, V. Lakshmikantham, D. O'Regan, A note on upper and lower solutions for first order inclusions of upper semicontinuous or lower semicontinuous type 12, 159--163 (2005), , Nonlinear Stud.
Remarques sur l'enlacement en théorie des points critiques pour des fonctionnelles continues
M. Frigon, Remarques sur l'enlacement en théorie des points critiques pour des fonctionnelles continues 47, 515--529 (2004), , Canad. Math. Bull.
Systems of coupled Poisson equations with critical growth in unbounded domains
F. Colin, M. Frigon, Systems of coupled Poisson equations with critical growth in unbounded domains CRM-2933, 10 (2003), , Rapport de recherche, CRM, Université de Montréal
A survey of recent fixed point theory in Fréchet spaces
R.P. Agarwal, M. Frigon, D. O'Regan, A survey of recent fixed point theory in Fréchet spaces 1, 2, 75--88 (2003), , Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday, Kluwer Acad. Publ., Dordrecht
Fixed points of cone-compressing and cone-extending operators in Fréchet spaces
M. Frigon, D. O'Regan, Fixed points of cone-compressing and cone-extending operators in Fréchet spaces 35, 672--680 (2003), , Bull. London Math. Soc.
Fixed point results for compact maps on closed subsets of Fréchet spaces and applications to differential and integral equations
M. Frigon, Fixed point results for compact maps on closed subsets of Fréchet spaces and applications to differential and integral equations 9, 23--37 (2002), , Bull. Belg. Math. Soc. Simon Stevin
Fixed point results for multivalued contractions on gauge spaces
M. Frigon, Fixed point results for multivalued contractions on gauge spaces 4, 175--181 (2002), , Set valued mapping with applications in nonlinear analysis, Ser. Math. Anal. Appl., Taylor and Francis, London
A Leray-Schauder alternative for Mönch maps on closed subsets of Fréchet spaces
M. Frigon, D. O'Regan, A Leray-Schauder alternative for Mönch maps on closed subsets of Fréchet spaces 21, 753--760 (2002), , Z. Anal. Anwendungen
Fuzzy contractive maps and fuzzy fixed points
M. Frigon, D. O'Regan, Fuzzy contractive maps and fuzzy fixed points 129, 39--45 (2002), , Fuzzy Sets and Systems
On a generalized critical point theory on gauge spaces and applications to ellliptic problems on $\Bbb R^N$
M. Frigon, On a generalized critical point theory on gauge spaces and applications to ellliptic problems on $\Bbb R^N$ 17, 67--89 (2001), , Topol. Methods Nonlinear Anal.
Second order Sturm-Liouville BVP's with impulses at variable moments
M. Frigon, D. O'Regan, Second order Sturm-Liouville BVP's with impulses at variable moments 8, 149--159 (2001), , Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal.
Fixed point results for generalized contractions in gauge spaces and applications
M. Frigon, Fixed point results for generalized contractions in gauge spaces and applications 128, 2957--2965 (electronic) (2000), , Proc. Amer. Math. Soc.
First order impulsive initial and periodic problems with variable moments
M. Frigon, D. O'Regan, First order impulsive initial and periodic problems with variable moments 233, 730--739 (1999), , J. Math. Anal. Appl.
On a new notion of linking and application to elliptic problems at resonance
M. Frigon, On a new notion of linking and application to elliptic problems at resonance 153, 96--120 (1999), , J. Differential Equations
Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet
M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet 22, 161--168 (1998), , Ann. Sci. Math. Québec
On a critical point theory for multivalued functionals and application to partial differential inclusions
M. Frigon, On a critical point theory for multivalued functionals and application to partial differential inclusions 31, 735--753 (1998), , Nonlinear Anal.
Nonlinear first-order initial and periodic problems in Banach spaces
M. Frigon, D. O'Regan, Nonlinear first-order initial and periodic problems in Banach spaces 10, 41--46 (1997), , Appl. Math. Lett.
Impulsive differential equations with variable times
M. Frigon, D. O'Regan, Impulsive differential equations with variable times 26, 1913--1922 (1996), , Nonlinear Anal.
On continuation methods for contractive and nonexpansive mappings
M. Frigon, On continuation methods for contractive and nonexpansive mappings 48, 19--30 (1996), , Recent advances on metric fixed point theory (Seville, 1995), Ciencias, Univ. Sevilla, Seville
Differential inclusions and implicit equations on closed subsets of $\Bbb R^n$
M. Frigon, L. Gorniewicz et T.
Kaczynski, Differential inclusions and implicit equations on closed subsets of $\Bbb R^n$ I-IV, 1797--1806 (1996), , World Congress of Nonlinear Analysts '92, (Tampa, Fl, 1992), de Gruyter, Berlin
Existence results for first-order impulsive differential equations
M. Frigon, D. O'Regan, Existence results for first-order impulsive differential equations 193, 96--113 (1995), , J. Math. Anal. Appl.
Topological methods in differential equations and inclusions
A. Grans, M. Frigon Eds, Topological methods in differential equations and inclusions 472, (1995), , NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Kluwer Acad. Publ., Dordrecht
Théorèmes d'existence de solutions d'inclusions différentielles
M. Frigon, Théorèmes d'existence de solutions d'inclusions différentielles 472, 51--87 (1995), , Topological methods in differential equations and inclusions (Montreal, PQ, 1994), NATO Adv. Sci. Inst. Ser.~C Math. Phys. Sci., Kluwer Acad. Publ., Dordrecht
Boundary and periodic value problems for systems of differential equations under Bernstein-Nagumo growth condition
M. Frigon, Boundary and periodic value problems for systems of differential equations under Bernstein-Nagumo growth condition 8, 1789--1804 (1995), , Differential Integral Equations
Boundary value problems for second order impulsive differential equations using set-valued maps
M. Frigon, D. O'Regan, Boundary value problems for second order impulsive differential equations using set-valued maps 58, 325--333 (1995), , Appl. Anal.
Existence theory for compact and noncompact intervals
M. Frigon, D. O'Regan, Existence theory for compact and noncompact intervals 2, 75--82 (1995), , Comm. Appl. Nonlinear Anal.
Existence results for some initial and boundary value problems without growth restriction
M. Frigon, D. O'Regan, Existence results for some initial and boundary value problems without growth restriction 123, 207--216 (1995), , Proc. Amer. Math. Soc.
Alternative non linéaire pour les applications contractantes
M. Frigon, A. Granas, Z.E.A. Guennoun, Alternative non linéaire pour les applications contractantes 19, 65--68 (1995), , Ann. Sci. Math. Québec
Existence results for initial value problems in Banach spaces
M. Frigon, D. O'Regan, Existence results for initial value problems in Banach spaces 2, 41--48 (1994), , Differential Equations Dynam. Systems
Résultats du type de Leray-Schauder pour des contractions multivoques
M. Frigon, A. Granas, Résultats du type de Leray-Schauder pour des contractions multivoques 4, 197--208 (1994), , Topol. Methods Nonlinear Anal.
Boundary and periodic value problems for systems differential equations under Bernstein-Nagumo growth condition
M. Frigon, Boundary and periodic value problems for systems differential equations under Bernstein-Nagumo growth condition CRM-2184, 22 (1994), , Rapport de recherche, CRM, Université de Montréal
Existence results for first order impulsive differential equations
M. Frigon, D. O'Regan, Existence results for first order impulsive differential equations DMS-358, 15 (1993), , Rapport de recherche, Université de Montréal
Boundary value problems for second order impulsive differential equations using set-valued maps
M. Frigon, D. O'Regan, Boundary value problems for second order impulsive differential equations using set-valued maps DMS-357, 9 (1993), , Rapport de recherche, Université de Montréal
Existence results for some initial and boundary value problems without growth restriction
M. Frigon, D. O'Regan, Existence results for some initial and boundary value problems without growth restriction DMS-359, 10 (1993), , Rapport de recherche, Université de Montréal
Boundary value problems for systems of implicit differential equations
M. Frigon, T. Kaczynski, Boundary value problems for systems of implicit differential equations 179, 317--326 (1993), , J. Math. Anal. Appl.
A note on the Cauchy problem for differential inclusions
M. Frigon, A. Granas, Z.E.A. Guennoun, A note on the Cauchy problem for differential inclusions 1, 315--321 (1993), , Topol. Methods Nonlinear Anal.
Some general existence principles for ordinary differential equations
M. Frigon, D. O'Regan, Some general existence principles for ordinary differential equations 2, 35--54 (1993), , Topol. Methods Nonlinear Anal.
Boundary and periodic value problems for systems of nonlinear second order differential equations
M. Frigon, Boundary and periodic value problems for systems of nonlinear second order differential equations 1, 259--274 (1993), , Topol. Methods Nonlinear Anal.
Théorèmes d'existence pour des problèmes aux limites sans condition de croissance
M. Frigon, Théorèmes d'existence pour des problèmes aux limites sans condition de croissance 117, 377--400 (1993), , Bull. Sci. Math.
Existence principles for Carathéodory differential equations in Banach spaces
M. Frigon, J.W. Lee, Existence principles for Carathéodory differential equations in Banach spaces 1, 95--111 (1993), , Topol. Methods Nonlinear Anal.
Boundary and periodic value problems for systems of nonlinear second order differential equations
M. Frigon, Boundary and periodic value problems for systems of nonlinear second order differential equations CRM-1802, 22 (1992), , Rapport de recherche, CRM, Université de Montréal
Boundary value problems for systems of implicit differential equations
M. Frigon, T. Kaczynski, Boundary value problems for systems of implicit differential equations DMS 92-1, 14 (1992), , Rapport de recherche, Université de Montréal
Problèmes aux limites pour des inclusions différentielles de type semi-continues inférieurement
M. Frigon, A. Granas, Problèmes aux limites pour des inclusions différentielles de type semi-continues inférieurement 17, 87--97 (1992) (1991), , Riv. Mat. Univ. Parma (4)
Heat equations with discontinuous nonlinearities on convex and nonconvex constraints
M. Frigon, C. Saccon, Heat equations with discontinuous nonlinearities on convex and nonconvex constraints 17, 923--946 (1991), , Nonlinear Anal.
Problèmes aux limites pour des inclusions différentielles sans condition de croissance
M. Frigon, Problèmes aux limites pour des inclusions différentielles sans condition de croissance 54, 69--83 (1991), , Ann. Polon. Math.
Problèmes aux limites pour des inclusions différentielles de type semi-continues inférieurement
M. Frigon, A. Granas, Problèmes aux limites pour des inclusions différentielles de type semi-continues inférieurement DMS 90-11, 16 (1990), , Rapport de recherche, Université de Montréal
On the Cauchy problem for differential inclusions
M. Frigon, A. Granas, Z.E.A. Guennoun, On the Cauchy problem for differential inclusions MATH-12, 13 (1990), , Rapport de recherche, Université de Monton
Heat equations with discontinuous nonlinearities on convex and nonconvex constraints
M. Frigon, C. Saccon, Heat equations with discontinuous nonlinearities on convex and nonconvex constraints vol 2.24.(485), 29 (1990), , Rapport de recherche, Università di Pisa
Théorèmes d'existence pour des inclusions différentielles sans convexité
M. Frigon, A. Granas, Théorèmes d'existence pour des inclusions différentielles sans convexité DMS 90-3, 8 (1990), , Rapport de recherche, Université de Montréal
Problèmes aux limites pour des inclusions différentielles sans condition de croissance
M. Frigon, Problèmes aux limites pour des inclusions différentielles sans condition de croissance CRM-1657, 24 (1990), , Rapport de recherche, Université de Montréal
Sur l'existence de solutions pour l'équation différentielle $u'(z)=f(z,u(z))$ dans un domaine complexe
M. Frigon, Sur l'existence de solutions pour l'équation différentielle $u'(z)=f(z,u(z))$ dans un domaine complexe 310, 371--374 (1990), , C. R. Acad. Sci. Paris Sér. I Math.
Théorèmes d'existence pour des inclusions différentielles sans convexité
M. Frigon, A. Granas, Théorèmes d'existence pour des inclusions différentielles sans convexité 310, 819--822 (1990), , C. R. Acad. Sci. Paris Sér. I Math.
Some remarks on the interval of existence of solutions to first order initial value problems
M. Frigon, D. O'Regan, Some remarks on the interval of existence of solutions to first order initial value problems 37, 199--206 (1990), , Utilitas Math.
Application de la théorie de la transversalité topologique à des problèmes non linéaires pour des équations différentielles ordinaires
M. Frigon, Application de la théorie de la transversalité topologique à des problèmes non linéaires pour des équations différentielles ordinaires 296, 75 (1990), , Dissertationes Math. (Rozprawy Mat.)
Some problems of parabolic type with discontinuous nonlinearities on convex constraints
M. Frigon, A. Marino, C. Saccon, Some problems of parabolic type with discontinuous nonlinearities on convex constraints 1, 41--52 (1990), , Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.
On a generalization of a theorem of S. Bernstein
M. Frigon, D. O'Regan, On a generalization of a theorem of S. Bernstein 48, 297--306 (1988), , Ann. Polon. Math.
Sur l'intervalle maximal d'existence de solutions pour des inclusions différentielles
M. Frigon, A. Granas, Z.E.A. Guennoun, Sur l'intervalle maximal d'existence de solutions pour des inclusions différentielles 306, 747--750 (1988), , C. R. Acad. Sci. Paris Sér. I Math.
