Electron. J. Diff. Equ., Vol. 2012 (2012), No. 49, pp. 1-19.

Evolution equations in generalized Stepanov-like pseudo almost automorphic spaces

Toka Diagana

In this article, first we introduce and study the concept of $\mathbb{S}_{\gamma}^p$-pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy), which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in $\mathbb{S}_{\gamma}^p$-pseudo almost automorphic spaces. To illustrate our abstract result, we will study the existence and uniqueness of a pseudo almost automorphic solution to the heat equation with a negative time-dependent diffusion coefficient.

Submitted February 1, 2012. Published March 27, 2012.
Math Subject Classifications: 58D25, 58D25, 43A60, 35B15, 42A75, 37L05.
Key Words: Pseudo almost automorphic; Stepanov-like; almost automorphic.

Show me the PDF file (289 KB), TEX file, and other files for this article.

Toka Diagana
Department of Mathematics, Howard University
2441 6th Street N.W.
Washington, DC 20059, USA
email: tdiagana@howard.edu

Return to the EJDE web page