WEIGHTED PSEUDO ALMOST AUTOMORPHIC MILD SOLUTIONS TO SEMILINEAR INTEGRAL EQUATIONS WITH S~p-WEIGHTED PSEUDO ALMOST AUTOMORPHIC COEFFICIENTS

摘要

In this paper, we consider the existence of weighted pseudo almost automorphic solutions of the semilinear integral equation x(t) - ∫_(-∞)~t a(t -s)[Ax(s) + f(s,x(s))]ds, t ∈ R in a Banach space X, where a ∈ L~1(R_+), A is the generator of an integral resolvent family of linear bounded operators defined on the Banach space X, and f : R×X → X is a weighted pseudo almost automorphic function. The main results are proved by using integral resolvent families, suitable composition theorems combined with the theory of fixed points.