Weyl-almost periodic solutions and asymptotically Weyl-almost periodic solutions of abstract Volterra integro-differential equations

Abstract

The main purpose of this article is to investigate Weyl-almost periodic solutions and asymptotically Weyl-almost periodic solutions of abstract Volterra integro-differential equations and inclusions. The class of asymptotically Weyl-almost periodic functions that we introduce here seems not to have been considered elsewhere, even in the scalar-valued case. We analyze the Weyl-almost periodic and asymptotically Weyl-almost periodic properties of convolution products and various types of degenerate solution operator families subgenerated by multivalued linear operators.