Existence of Square-Mean Almost Automorphic Solutions to Stochastic Functional Integrodifferential Equations in Hilbert SpacesReport as inadecuate




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Abstract and Applied AnalysisVolume 2014 2014, Article ID 480241, 10 pages

Research ArticleSchool of Mathematics and Information Sciences, Yulin Normal University, Yulin 537000, China

Received 20 December 2013; Accepted 13 February 2014; Published 27 March 2014

Academic Editor: Yonghuia Xia

Copyright © 2014 Lijie Li. 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

The existence and uniqueness of square-mean almost automorphic mild solution to a stochastic functional integrodifferential equation is studied. Under some appropriate assumptions, the existence and uniqueness of square-mean almost automorphic mild solution is obtained by Banach’s fixed point theorem. Particularly, based on Schauder’s fixed point theorem, the existence of square-mean almost automorphic mild solution is obtained by using the condition which is weaker than Lipschitz conditions. Finally, an example illustrating our main result is given.





Author: Lijie Li

Source: https://www.hindawi.com/



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