Hammerstein integral inclusions in reflexive Banach spaces

Abstract

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.