Abstract and Applied Analysis

On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

Jing Cui and Litan Yan

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Abstract

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 870831, 25 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495769

Digital Object Identifier
doi:10.1155/2012/870831

Mathematical Reviews number (MathSciNet)
MR2947717

Zentralblatt MATH identifier
1257.34044

Citation

Cui, Jing; Yan, Litan. On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations. Abstr. Appl. Anal. 2012 (2012), Article ID 870831, 25 pages. doi:10.1155/2012/870831. https://projecteuclid.org/euclid.aaa/1355495769


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