Electron. J. Diff. Equ., Vol. 2013 (2013), No. 188, pp. 1-20.

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

Toka Diagana, Mohamed Zitane

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.

Submitted May 23, 2013. Published August 28, 2013.
Math Subject Classifications: 34C27, 35B15, 46E30.
Key Words: Pseudo-almost automorphy; $S^{p,q(x)}$-pseudo-almost automorphic; Lebesgue space with variable exponents; variable exponents.

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Toka Diagana
Department of Mathematics, Howard University
2441 6th Street NW, Washington, DC 20059, USA
email: tokadiag@gmail.com
Mohamed Zitane
Université Ibn Tofaïl, Faculté des Sciences
Département de Mathématiques, Laboratoire d'An. Maths et GNC
B.P. 133, Kénitra 1400, Maroc
email: zitanem@gmail.com

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