Existence of random mild solutions of a random integrodifferential equation with lack of compactness

Abstract

In this paper, we show the existence of random mild solutions for a broad class of random integrodifferential equations with lack of compactness. The results are obtained using noncompact resolvent operators and a fixed point theorem of Monch type. Our results are applied to a large variety of partial differential equations in which memory effects are considered. Some examples are provided to illustrate the theoretical results. Mathematics Subject Classification (2010). Primary 45K05, 47G20, 47D06, 47H10; Secondary 47H08.