ASYMPTOTICALLY TYPED SOLUTIONS TO A SEMILINEAR INTEGRAL EQUATION

摘要

In this paper, we investigate the existence of mu-pseudo almost automorphic solutions to the semilinear integral equation x (t) = integral(t)(-infinity) a(t - s)[Ax(s) + f(s; x(s))] ds, t is an element of R in a Banach space X, where a is an element of 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 -> X is a mu-pseudo almost automorphic function. The main results are proved by using integral resolvent families combined with the theory of mu-pseudo almost automorphic functions.