Abstract and Applied Analysis
Volume 2012 (2012), Article ID 179525, 15 pages
http://dx.doi.org/10.1155/2012/179525
Research Article

Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations

Jun Zhang,1 Ti-Jun Xiao,2 and Jin Liang3

1School of Mathematics and Statistics, Central China Normal University, Hubei, Wuhan 430079, China
2Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
3Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received 24 December 2011; Accepted 9 January 2012

Academic Editor: Josef Diblík

Copyright © 2012 Jun Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation: x′(t)=Ax(t)+f(t,x(t)), t∈ℝ, where A is the infinitesimal generator of an exponentially stable C0-semigroup. An application is also given to illustrate the abstract existence theorem.