Electron. J. Diff. Equ., Vol. 2014 (2014), No. 236, pp. 1-15.

Composition of S^p-weighted pseudo almost automorphic functions and applications

Chuan-Hua Chen, Hong-Xu Li

Abstract:
Since the background space of S^p-weighted pseudo almost automorphic functions (abbr. S^p-wpaa functions) is endowed with a norm coming from L^p norm, it is natural to consider the composition of S^p-wpaa functions under conditions of L^p norm. However, the known resutls for composition of S^p-wpaa functions were always given under conditions of supremum norm. Motivated by this, we establish some new results for the composition of S^p-almost automorphic functions and S^p-wpaa functions under a "uniform continuity condition" with respect to L^p norm. As an application, we prove the existence of mild weighted pseudo almost automorphic solutions for some semilinear differential equations with an S^p-wpaa force term. An example of the heat equation illustrates our results.

Submitted September 17, 2014. Published November 06, 2014.
Math Subject Classifications: 43A60, 34G20, 47D03.
Key Words: S^p-almost automorphic; uniform continuity; S^p-weighted pseudo almost automorphic; semilinear differential equation.

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Chuan-Hua Chen
Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: chenchuanhua8@163.com
Hong-Xu Li
Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: hoxuli@scu.edu.cn

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