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# Frigon, Marlène

Professeure titulaire

Faculté des arts et des sciences - Département de mathématiques et de statistique

514 343-2316

### Affiliations

• Membre Centre de recherches mathématiques
• Membre CRM  Centre de recherches mathématiques

### Expertise

Mes travaux portent principalement sur la théorie des points fixes et la théorie des points critiques ainsi que sur l'application de ces théories aux équations et inclusions différentielles ordinaires ou partielles.

### Publications choisies Tout déplierTout replier

#### 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.