Marlene Frigon - Academia.edu (original) (raw)

Papers by Marlene Frigon

Advanced Nonlinear Studies

In this article, we establish existence and multiplicity results for first-order Stieltjes differ... more In this article, we establish existence and multiplicity results for first-order Stieltjes differential equations satisfying a periodic boundary condition or an initial value condition. No monotonicity condition involving the right-hand side f f is imposed at the discontinuity points of the derivator g g . Our results rely on the fixed point index theory and new notions of strict lower and upper solutions. An application to a population model with an extreme event is presented to study the persistence of a species.

In this paper, using the Schauder Fixed Point Theorem, we establish some existence results to bou... more In this paper, using the Schauder Fixed Point Theorem, we establish some existence results to boundary and periodic value problems for systems of nonlinear second order differential equations. Also, the notion of upper and lower solutions to a differential equation is generalized in a natural way to systems of differential equations.

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2002

In this paper, we establish fixed point results for compact maps f : X → E defined on arbitrary c... more In this paper, we establish fixed point results for compact maps f : X → E defined on arbitrary closed subsets X of a Fréchet space E. In particular, we obtain a continuation principle for suitable compact homotopy h : X × [0, 1] → E. Afterwards, those results are applied to differential equations and to Fredholm integral equations on the real line.

World Congress of Nonlinear Analysts '92, 1996

Google, Inc. (search). ...

We present fixed point results for admissibly compact maps on cones in Fr´echet spaces. We first ... more We present fixed point results for admissibly compact maps on cones in Fr´echet spaces. We first extend the Krasnosel’ski˘i fixed point theorem with order type cone-compression and cone-expansion conditions. Then, we extend the monotone iterative method to this context. Finally, we present fixed point results under a combination of the assumptions of the previous results. More precisely, we combine a cone-compressing or cone-extending condition only on one side of the boundary of an annulus with an assumption on the existence of an upper fixed point. In addition, we show that the usual monotonicity condition can be weaken

Topological methods in nonlinear analysis

Equazioni a derivate parziali.-Some problems of parabolic type with discontinuous nonlinearities ... more Equazioni a derivate parziali.-Some problems of parabolic type with discontinuous nonlinearities on convex constraints. Nota (*) di MARLENE FRIGON, ANTONIO MARINO e CLAUDIO SACCON, presentata dal Socio E. DE GIORGI. ABSTRACT.-We study semilinear equations and inequalities of parabolic type with discontinuous nonlinearities, possibly subjected to convex or even nonconvex constraint conditions. To prove some existence theorems we regard the solutions as «curves of maximal relaxed slope» for a suitable functional on the given constraint. KEY WORDS: Curves of maximal slope; Partial differential equations; Discontinuity; Nonconvex constraints. RIASSUNTO.-Alcuni problemi di tipo parabolico semilineare con termini non lineari discontinui su vincoli non convessi. Si studiano alcune equazioni e disequazioni di tipo parabolico semilineare con termine non lineare discontinuo, in presenza di condizioni di vincolo anche non convesse. Per ottenere dei teoremi di esistenza si interpretano le soluzioni come «curve di massima pendenza rilassata» per un opportuno funzionale sul vincolo considerato.

Topological Methods in Differential Equations and Inclusions, 1995

Proceedings of the American Mathematical Society, 1995

In this paper, using the Schauder Fixed Point Theorem, we establish some existence results or ini... more In this paper, using the Schauder Fixed Point Theorem, we establish some existence results or initial and boundary value problems for differential equations withouth growth restriction on the right member. In §3 we examine the existence of solutions for a first-order initial value

Nonlinear Analysis: Theory, Methods & Applications, 1996

Nonlinear Analysis: Theory, Methods & Applications, 2007

In this paper, we establish the existence of solutions to systems of first order differential inc... more In this paper, we establish the existence of solutions to systems of first order differential inclusions with maximal monotone terms satisfying the periodic boundary condition. Our proofs rely on the theory of maximal monotone operators, and the Schauder and the Kakutani fixed point theorems. A notion of solutiontube to these problems is introduced. This notion generalizes the notion of upper and lower solutions of first order differential equations.

Nonlinear Analysis: Theory, Methods & Applications, 1998

Nonlinear Analysis: Theory, Methods & Applications, 1991

Nonlinear Differential Equations and Applications NoDEA, 2006

Journal of Mathematical Analysis and Applications, 1995

Journal of Mathematical Analysis and Applications, 1999

Journal of Mathematical Analysis and Applications, 1993

Journal of Fixed Point Theory and Applications, 2007

Journal of Fixed Point Theory and Applications, 2011