Existence Results for Some Nonautonomous Integro-differential Equations

TL;DR

This paper proves the existence of pseudo-almost automorphic solutions for certain nonautonomous integro-differential equations using operator theory and fixed-point theorems, with applications to biological models.

Contribution

It introduces new existence results for pseudo-almost automorphic solutions to nonautonomous integro-differential equations using advanced mathematical tools.

Findings

Existence of solutions for specific integro-differential equations established.

Application to models in population genetics and nerve pulse propagation demonstrated.

Utilizes Schauder fixed-point theorem and operator theory techniques.

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.