Existence of generalized almost periodic and asymptotic almost periodic solutions to abstract volterra integro-differential equations

Abstract

© 2017 Texas State University. The main aim of this paper is to study the asymptotic almost periodicity, Stepanov almost periodicity, and asymptotic Stepanov almost periodicity of various classes of regularized solution operator families appearing in the theory of abstract Volterra integro-differential equations. Subgenerators of these solution operator families, which can be degenerate or non-degenerate in time, are multivalued linear operators. We contemplate the results established by many other authors, providing also a great number of original contributions, illustrative examples and applications of our abstract results.