Tiziana Cardinali

Hammerstein integral inclusions in reflexive Banach spaces

In this paper we examine multivalued Hammerstein integral equations defined in a separable reflexive Banach space. We prove existence theorems for both the “convex” problem (the multifunction is convex-valued) and the “nonconvex” problem (the multifunction is not necessarily convex-valued). We also show that the solution set of the latter is dense in the solution set of the former (relaxation theorem). Finally we present some examples illustrating the applicability of our abstract results.

Periodic solutions of nonlinear impulsive differential inclusions with constraints

In this paper we obtain the existence of periodic solutions for nonlinear invariance problems monitored by impulsive differential inclusions subject to impulse effects.

On the existence of solutions for nonlinear impulsive periodic viable problems

In this paper we prove the existence of periodic solutions for nonlinear impulsive viable problems monitored by differential inclusions of the type x′(t)∈F(t,x(t))+G(t,x(t)). Our existence theorems extend, in a broad sense, some propositions proved in [10] and improve a result due to Hristova-Bainov in [13].

Extremal solutions for nonlinear parabolic problems with discontinuities

AbstractThis paper examines nonlinear parabolic initial-boundary value problems with a discontinuous forcing term, which is locally of bounded variation. Assuming that there exist an upper solution φ and a lower solution Ψ, we prove the existence of a maximal and of a minimal solution within the order interval [ψ,ϕ]

Periodic problems and problems with discontinuities for nonlinear parabolic equations

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Two abstract approaches in vectorial fixed point theory

LP(P xZ). Our approach is based on a Jordan-type decomposition for the discontinuous forcing term and on a fixed point theorem for nondecreasing maps in ordered Banach spaces.

Nonlocal semilinear integro-differential inclusions via vectorial measures of noncompactness

In this note we investigate in Banach spaces the existence of mild solutions for initial problems, also in presence of impulses, governed by semilinear differential inclusions where the non-linear part is a Scorza-Dragoni multifunction. All the results are obtained via a generalization of {\it Artstein-Prikry selection theorem} that we obtain in the first part of the paper.

Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions

In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that their solution set is a compact Rδ-set in (CT, L2(Z)).