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

Volume 12, Number 1 (2011), 19 - 33

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

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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.