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Abstract and Applied Analysis
Volume 2014, Article ID 263690, 11 pages
http://dx.doi.org/10.1155/2014/263690
Research Article

Antiperiodic Problems for Nonautonomous Parabolic Evolution Equations

1Department of Applied Mathematics, Guangdong University of Foreign Studies, Guangzhou 510420, China
2Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, China

Received 10 April 2014; Accepted 4 May 2014; Published 22 May 2014

Academic Editor: Hui-Sheng Ding

Copyright © 2014 R. N. Wang and Y. Zhou. 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

This work focuses on the antiperiodic problem of nonautonomous semilinear parabolic evolution equation in the form , , , , where (possibly unbounded), depending on time, is a family of closed and densely defined linear operators on a Banach space . Upon making some suitable assumptions such as the Acquistapace and Terreni conditions and exponential dichotomy on , we obtain the existence results of antiperiodic mild solutions to such problem. The antiperiodic problem of nonautonomous semilinear parabolic evolution equation of neutral type is also considered. As sample of application, these results are applied to, at the end of the paper, an antiperiodic problem for partial differential equation, whose operators in the linear part generate an evolution family of exponential stability.