On the solution sets of differential inclusions and the periodic problem in Banach spaces (original) (raw)

Periodic solutions of a perturbed system of differential inclusions in Banach spaces

By means of the Hausdorff measure of noncompactness and the topological degree theory for condensing operator in locally convex spaces we show the existence of periodic solutions of a singularly perturbed system of differential inclusions in infinite dimensional Banach spaces. Moreover, the behaviour of such periodic solutions when the parameter tends to zero is also investigated.

The existence of periodic solutions to nonautonomous differential inclusions

Proceedings of the American Mathematical Society, 1988

For an m-dimensional differential inclusion of the form ie A(t)x(t) + F[t,x(t)], with A and F T-periodic in t, we prove the existence of a nonconstant periodic solution. Our hypotheses require m to be odd, and require F to have different growth behavior for |i| small and |i| large (often the case in applications). The idea is to guarantee that the topological degree associated with the system has different values on two distinct neighborhoods of the origin.

Periodic Solutions of a Singularly Perturbed System of Differential Inclusions in Banach Spaces

2001

By means of the Hausdorff measure of noncompactness and the topological degree theory for condensing operator in locally convex spaces we show the existence of periodic solutions of a singularly perturbed system of differential inclusions in infinite dimensional Banach spaces. Moreover, the behaviour of such periodic solutions when the parameter tends to zero is also investigated.

On boundary value problems for degenerate differential inclusions in Banach spaces

Abstract and Applied Analysis, 2003

We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of inclusions. Some particular cases including periodic problems are considered.

Almost-periodicity problem as a fixed-point problem for evolution inclusions

Topological methods in nonlinear analysis

Existence of almost-periodic solutions to quasi-linear evolution inclusions under a Stepanov almost-periodic forcing is nontraditionally examined by means of the Banach-like and the Schauder-Tikhonov-like fixedpoint theorems. These multivalued fixed-point principles concern condensing operators in almost-periodic function spaces or their suitable closed subsets. The Bohr-Neugebauer-type theorem jointly with the Bochner transform are employed, besides another, for this purpose. Obstructions related to possible generalizations are discussed.