In this article, first we introduce and study the concept of -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 -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.
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| Toka Diagana |
Department of Mathematics, Howard University
2441 6th Street N.W.
Washington, DC 20059, USA
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