Positive almost automorphic solutions for some nonlinear infinite delay integral equations, Dynamic Systems and Applications 17

ABSTRACT. We state sufficient conditions for the existence of positive bounded, almost auto-morphic or almost periodic solutions of the following nonlinear infinite delay integral equation: x(t) = t a(t, t − s)f(s, x(s)) ds. Then we apply these results to a finite delay integral equation when the delay is time-dependent and for a delay differential equation. AMS (MOS) Subject Classification. 42A75; 44A35, 45G10 1