Volterra and Functional Differential Equations

INTEGRODIFFERENTIAL EQUATIONS WITH ALMOST PERIODIC SOLUTIONS

C. Corduneanu

Department of Mathematics

University of Texas at Arlington

Arlington, Texas

DOI: 10.1201/9781003420026-17

1. INTRODUCTION

In a recent paper [8], we dealt with the existence of almost periodic solutions to certain classes of differential equations with infinite delay, which can be represented in the form

$$\stackrel{·}{\text{x}}\left(t\right)=\underset{0}{\overset{\infty }{{\displaystyle \int }}}\left[dA\left(s\right)\right]x\left(t-s\right)+f\left(t\right).$$ (0)

A(s) designates a square matrix of order n whose entries are real-valued functions with bounded variation on the positive half axis, while x and f stand for vector-valued functions with n real coordinates.

The aim of this paper is to point out that similar results hold true for a ...