STEPANOV-LIKE PSEUDO-ALMOST AUTOMORPHIC FUNCTIONS IN LEBESGUE SPACES WITH VARIABLE EXPONENTS Lp(x).

In this article we introduce and study a new class of functions called Stepanov-like pseudo-almost automorphic functions with variable exponents, which generalizes in a natural way classical Stepanov-like pseudo-almost automorphic spaces. Basic properties of these new spaces are investigated. The existence of pseudo-almost automorphic solutions to some first-order diffeerential equations with Sp,q(x)-pseudo-almost automorphic coefficients will also be studied. [ABSTRACT FROM AUTHOR]