Stepanov-like pseudo-almost automorphic functions in Lebesgue spaces with variable exponents L^{p(x)}

• Published in: Electronic journal of differential equations Vol. 2013; no. 188; pp. 1 - 20
• Main Authors: Toka Diagana, Mohamed Zitane
• Format: Journal Article
• Language: English
• Published: Texas State University 28-08-2013
• Subjects: Lebesgue space with variable exponents; Pseudo-almost automorphy; S^{p,q(x)}$-pseudo-almost automorphic; variable exponents
• ISSN: 1072-6691

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 differential equations with $S^{p,q(x)}$-pseudo-almost automorphic coefficients will also be studied.