Pseudo-almost periodic and pseudo-almost automorphic solutions to some evolution equations involving theoretical measure theory

Abstract

Motivated by the recent works by the first and the second named authors, in this paper we introduce the notion of doubly-weighted pseudo-almost periodicity (respectively, doubly-weighted pseudo-almost automorphy) using theoretical measure theory. Basic properties of these new spaces are studied. To illustrate our work, we study, under Acquistapace–Terreni conditions and exponential dichotomy, the existence of (μ,ν)- pseudo almost periodic (respectively, (μ,ν)-pseudo almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces. A few illustrative examples will be discussed at the end of the paper.