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2012 Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations
Jun Zhang, Ti-Jun Xiao, Jin Liang
Abstr. Appl. Anal. 2012: 1-15 (2012). DOI: 10.1155/2012/179525

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 ) = A x ( t ) + f ( t , x ( t ) ) , t \Bbb R , where A is the infinitesimal generator of an exponentially stable C 0 -semigroup. An application is also given to illustrate the abstract existence theorem.

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Jun Zhang. Ti-Jun Xiao. Jin Liang. "Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations." Abstr. Appl. Anal. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/179525

Information

Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1244.34083
MathSciNet: MR2903805
Digital Object Identifier: 10.1155/2012/179525

Rights: Copyright © 2012 Hindawi

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