Positive pseudo almost periodic solutions for some nonlinear infinite delay integral equations

We state sufficient conditions for the existence of positive pseudo almost periodic and asymptotically almost periodic solutions of the following nonlinear infinite delay integral equation: x ( t ) = ∫ − ∞ t a ( t , t − s ) f ( s , x ( s ) ) d s . Then we apply these results to a finite delay integral equation when the delay is time-dependent and to a delay differential equation.