irene Benedetti - Academia.edu (original) (raw)

Papers by irene Benedetti

Annali di Matematica Pura ed Applicata (1923 -)

We prove a global existence result for bounded solutions to a class of abstract semilinear delay ... more We prove a global existence result for bounded solutions to a class of abstract semilinear delay evolution equations with measures subjected to nonlocal initial data of the form du(t) = {Au(t) + f (t, u t)}dt + dg(t), t ∈ R + , u(t) = h(u)(t), t ∈ [ −τ, 0 ], where τ ≥ 0, A : D(A) ⊆ X → X is the infinitesimal generator of a C 0-semigroup, f : R + × R([ −τ, 0 ]; X) → X is continuous, g ∈ BV loc (R + ; X), and h : R b (R + ; X) → R([ −τ, 0 ]; X) is nonexpansive.

Journal of Fixed Point Theory and Applications

In this paper, fixed point arguments and a critical point technique are combined leading to hybri... more In this paper, fixed point arguments and a critical point technique are combined leading to hybrid existence results for a system of two operator equations where only one of the equations has a variational structure. An application to periodic solutions of a semi-variational system is given to illustrate the theory.

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an ... more We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an integro-differential inclusion in a Banach space with a non-densely defined operator. Since we look for integrated solution we do not need to assume that A is a Hille Yosida operator. We exploit a technique based on the measure of weak non-compactness which allows us to avoid any hypotheses of compactness both on the semigroup generated by the linear part and on the nonlinear term. As the main tool in the proof of our existence result, we are using the Glicksberg–Ky Fan theorem on a fixed point for a multivalued map on a compact convex subset of a locally convex topological vector space. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

Mathematica Bohemica

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Discrete & Continuous Dynamical Systems - S

Topological Methods in Nonlinear Analysis

By combining an approximation technique with the Leray-Schauder continuation principle, we prove ... more By combining an approximation technique with the Leray-Schauder continuation principle, we prove global existence results for semilinear differential equations involving a dissipative linear operator, generating an extendable compact C 0-semigroup of contractions, and a Carathéodory nonlinearity f : [0, T ] × E → F , with E and F two real Banach spaces such that E ⊆ F , besides imposing other conditions. The case E = F allows to treat, as an application, parabolic equations with continuous superlinear nonlinearities which satisfy a sign condition.

Fractional Calculus and Applied Analysis

We prove existence of mild solutions to a class of semilinear fractional differential inclusions ... more We prove existence of mild solutions to a class of semilinear fractional differential inclusions with non local conditions in a reflexive Banach space. We are able to avoid any kind of compactness assumptions both on the nonlinear term and on the semigroup generated by the linear part. We apply the obtained theoretical results to two diffusion models described by parabolic partial integro-differential inclusions.

Journal of Mathematical Analysis and Applications

The paper deals with second order parabolic equations on bounded domains with Dirichlet condition... more The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A linear diffusion term in divergence form is included which generates a strongly elliptic differential operator. A further linear part, of integral type, is present which accounts of nonlocal diffusion behaviours. The main result provides a unifying method for studying the existence and localization of solutions satisfying nonlocal associated boundary conditions. The Cauchy multipoint and the mean value conditions are included in this investigation. The problem is transformed into its abstract setting and the proofs are based on the homotopic invariance of the Leray-Schauder topological degree. A bounding function (i.e. Lyapunov-like function) theory is developed, which is new in this infinite dimensional context. It allows that the associated vector fields have no fixed points on the boundary of their domains and then it makes possible the use of a degree argument.

Differential Equations and Dynamical Systems

Topological Methods in Nonlinear Analysis

Fundamenta Informaticae, 2017

Discrete and Continuous Dynamical Systems, 2017

The existence of mild solutions is obtained, for a semilinear multivalued equation in a reflexive... more The existence of mild solutions is obtained, for a semilinear multivalued equation in a reflexive Banach space. Weakly compact valued nonlinear terms are considered, combined with strongly continuous evolution operators generated by the linear part. A continuation principle or a fixed point theorem are used, according to the various regularity and growth conditions assumed. Applications to the study of parabolic and hyperbolic partial differential equations are given.

Fixed Point Theory, 2014

We investigate a generalization of midpoint convexity for multivalued maps, and derive fixed poin... more We investigate a generalization of midpoint convexity for multivalued maps, and derive fixed points theorems under this more general assumption without requiring any strong compactness condition. As an application we prove the existence of social equilibria for games with n players.

Topological Methods in Nonlinear Analysis, 2015

Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015

An existence result for differential inclusions in a separable Hilbert space is furnished. A wide... more An existence result for differential inclusions in a separable Hilbert space is furnished. A wide family of nonlocal boundary value problems is treated, including periodic, anti-periodic, mean value and multipoint conditions. The study is based on an approximation solvability method. Advanced topological methods are used as well as a Scorza Dragoni-type result for multivalued maps. The conclusions are original also in the single-valued setting. An application to a nonlocal dispersal model is given.

Topological Methods in Nonlinear Analysis, 2008

In this paper we deal with impulsive Cauchy problems in Banach spaces governed by a delay semilin... more In this paper we deal with impulsive Cauchy problems in Banach spaces governed by a delay semilinear differential inclusion y ∈ A(t)y +F (t, yt). The family {A(t)} t∈[0,b] of linear operators is supposed to generate an evolution operator and F is a upper Carathèodory type multifunction. We first provide the existence of mild solutions on a compact interval and the compactness of the solution set. Then we apply this result to obtain the existence of mild solutions for the impulsive Cauchy problem on non-compact intervals.

Communications in Contemporary Mathematics, 2016

A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated... more A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations. It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions technique. No compactness or condensivity condition on the nonlinearities is assumed. Some applications of the abstract result to the study of nonlocal problems for integro-differential equations and systems of integro-differential equations are then showed. A generalization of the result by using nonsmooth bounding functions is given.

Journal of Applied Analysis, 2010

Journal of Function Spaces, 2015

We provide existence results for a fractional differential inclusion with nonlocal conditions and... more We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.

Annali di Matematica Pura ed Applicata (1923 -)

We prove a global existence result for bounded solutions to a class of abstract semilinear delay ... more We prove a global existence result for bounded solutions to a class of abstract semilinear delay evolution equations with measures subjected to nonlocal initial data of the form du(t) = {Au(t) + f (t, u t)}dt + dg(t), t ∈ R + , u(t) = h(u)(t), t ∈ [ −τ, 0 ], where τ ≥ 0, A : D(A) ⊆ X → X is the infinitesimal generator of a C 0-semigroup, f : R + × R([ −τ, 0 ]; X) → X is continuous, g ∈ BV loc (R + ; X), and h : R b (R + ; X) → R([ −τ, 0 ]; X) is nonexpansive.

Journal of Fixed Point Theory and Applications

In this paper, fixed point arguments and a critical point technique are combined leading to hybri... more In this paper, fixed point arguments and a critical point technique are combined leading to hybrid existence results for a system of two operator equations where only one of the equations has a variational structure. An application to periodic solutions of a semi-variational system is given to illustrate the theory.

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an ... more We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an integro-differential inclusion in a Banach space with a non-densely defined operator. Since we look for integrated solution we do not need to assume that A is a Hille Yosida operator. We exploit a technique based on the measure of weak non-compactness which allows us to avoid any hypotheses of compactness both on the semigroup generated by the linear part and on the nonlinear term. As the main tool in the proof of our existence result, we are using the Glicksberg–Ky Fan theorem on a fixed point for a multivalued map on a compact convex subset of a locally convex topological vector space. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

Mathematica Bohemica

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Discrete & Continuous Dynamical Systems - S

Topological Methods in Nonlinear Analysis

By combining an approximation technique with the Leray-Schauder continuation principle, we prove ... more By combining an approximation technique with the Leray-Schauder continuation principle, we prove global existence results for semilinear differential equations involving a dissipative linear operator, generating an extendable compact C 0-semigroup of contractions, and a Carathéodory nonlinearity f : [0, T ] × E → F , with E and F two real Banach spaces such that E ⊆ F , besides imposing other conditions. The case E = F allows to treat, as an application, parabolic equations with continuous superlinear nonlinearities which satisfy a sign condition.

Fractional Calculus and Applied Analysis

We prove existence of mild solutions to a class of semilinear fractional differential inclusions ... more We prove existence of mild solutions to a class of semilinear fractional differential inclusions with non local conditions in a reflexive Banach space. We are able to avoid any kind of compactness assumptions both on the nonlinear term and on the semigroup generated by the linear part. We apply the obtained theoretical results to two diffusion models described by parabolic partial integro-differential inclusions.

Journal of Mathematical Analysis and Applications

The paper deals with second order parabolic equations on bounded domains with Dirichlet condition... more The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A linear diffusion term in divergence form is included which generates a strongly elliptic differential operator. A further linear part, of integral type, is present which accounts of nonlocal diffusion behaviours. The main result provides a unifying method for studying the existence and localization of solutions satisfying nonlocal associated boundary conditions. The Cauchy multipoint and the mean value conditions are included in this investigation. The problem is transformed into its abstract setting and the proofs are based on the homotopic invariance of the Leray-Schauder topological degree. A bounding function (i.e. Lyapunov-like function) theory is developed, which is new in this infinite dimensional context. It allows that the associated vector fields have no fixed points on the boundary of their domains and then it makes possible the use of a degree argument.

Differential Equations and Dynamical Systems

Topological Methods in Nonlinear Analysis

Fundamenta Informaticae, 2017

Discrete and Continuous Dynamical Systems, 2017

The existence of mild solutions is obtained, for a semilinear multivalued equation in a reflexive... more The existence of mild solutions is obtained, for a semilinear multivalued equation in a reflexive Banach space. Weakly compact valued nonlinear terms are considered, combined with strongly continuous evolution operators generated by the linear part. A continuation principle or a fixed point theorem are used, according to the various regularity and growth conditions assumed. Applications to the study of parabolic and hyperbolic partial differential equations are given.

Fixed Point Theory, 2014

We investigate a generalization of midpoint convexity for multivalued maps, and derive fixed poin... more We investigate a generalization of midpoint convexity for multivalued maps, and derive fixed points theorems under this more general assumption without requiring any strong compactness condition. As an application we prove the existence of social equilibria for games with n players.

Topological Methods in Nonlinear Analysis, 2015

Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain), 2015

An existence result for differential inclusions in a separable Hilbert space is furnished. A wide... more An existence result for differential inclusions in a separable Hilbert space is furnished. A wide family of nonlocal boundary value problems is treated, including periodic, anti-periodic, mean value and multipoint conditions. The study is based on an approximation solvability method. Advanced topological methods are used as well as a Scorza Dragoni-type result for multivalued maps. The conclusions are original also in the single-valued setting. An application to a nonlocal dispersal model is given.

Topological Methods in Nonlinear Analysis, 2008

In this paper we deal with impulsive Cauchy problems in Banach spaces governed by a delay semilin... more In this paper we deal with impulsive Cauchy problems in Banach spaces governed by a delay semilinear differential inclusion y ∈ A(t)y +F (t, yt). The family {A(t)} t∈[0,b] of linear operators is supposed to generate an evolution operator and F is a upper Carathèodory type multifunction. We first provide the existence of mild solutions on a compact interval and the compactness of the solution set. Then we apply this result to obtain the existence of mild solutions for the impulsive Cauchy problem on non-compact intervals.

Communications in Contemporary Mathematics, 2016

A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated... more A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations. It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions technique. No compactness or condensivity condition on the nonlinearities is assumed. Some applications of the abstract result to the study of nonlocal problems for integro-differential equations and systems of integro-differential equations are then showed. A generalization of the result by using nonsmooth bounding functions is given.

Journal of Applied Analysis, 2010

Journal of Function Spaces, 2015

We provide existence results for a fractional differential inclusion with nonlocal conditions and... more We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.