Positive Pseudo Almost Automorphic Solutions for Some Nonlinear Infinite Delay Integral Equations

Abstract

We state sufficient conditions for the existence of positive pseudo almost automorphic solutions of the following nonlinear infinite delay integral equation:

$$ x(t)= \int^t_{-\infty}a(t,t-s)f(s,x(s))\: ds . $$

We deduce some corollaries on a finite delay integral equation and on a delay differential equation.