Periodic solutions for a class of differential inclusions in general Banach spaces

摘要

Let X be a real Banach space, A: D(A) subset of X hooked right arrow X an m-accretive operator and F: R x <(D(A))over bar>) hooked right arrow X a multi-function which is 2 pi-periodic with respect to its first argument, has nonempty, closed, convex and weakly compact values and is strongly-weakly upper semicontinuous. In this paper we prove the existence of at least one solution for the problem {u'(t) + Au(t) superset of f(t), f(t) is an element of F(t, u(t)), u(t) = u(t + 2 pi), in the case in which F satisfies an appropriate "sign" condition. (c) 2007 Elsevier Inc. All fights reserved.