Weighted Stepanov-Like Pseudo-Almost Periodic Functions in Lebesgue Space with Variable Exponents $L^{p(x)}$

Abstract

In this paper we introduce and study a new class of functions called $S^{p,q(x)}$pseudo-almost periodic (or weighted Stepanov-like pseudo-almost periodic functions with variable exponents), which generalizes the class of weighted Stepanov-like pseudo-almost periodic functions. Basic properties of these new spaces are established. The existence of weighted pseudo-almost periodic solutions to some first-order differential equations with $S^{p,q(x)}$pseudo-almost periodic coefficients will also be studied.