SP-ALMOST PERIODIC AND SP-ALMOST AUTOMORPHIC SOLUTIONS OF AN INTEGRAL EQUATION WITH INFINITE DELAY

We state sufficient conditions for the existence and uniqueness of Stepanov-like pseudo almost periodic and Stepanov-like pseudo almost automorphic solutions for a class of nonlinear Volterra integral with infinite delay of the form x(t) - f(t,x(t)x x(t - r(t))) - integral(+infinity)(t) c(t, s)g(s,x(s), x(s - r(s)))ds. Our approach is based on Bochner's transform, some analytic techniques, and a Banach fixed point theorem. Then we apply these results to a nonlinear differential equation when the delay is time -dependent and the force function is continuous x '(t) = ax(t) + ax '(t - r(t)) - q(t,x(t), x(t - r(t))) + h(t).