Existence Results for Some Nonautonomous Integro-differential Equations

Abstract

In this paper we make a subtle use of tools from operator theory and the Schauder fixed-point theorem to establish the existence of pseudo-almost automorphic solutions to some classes of nonautonomous integro-differential equations with pseudo-almost automorphic forcing terms. To illustrate our main results, the existence of pseudo-almost automorphic solutions to a parabolic Neumann boundary value problem that models population genetics and nerve pulse propagation will be discussed.