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Existence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delays

 

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Opened Access Existence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delays
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Author: Diop, Mamadou Abdoul
Caraballo Garrido, Tomás
Zene, Mahamat Mahamat
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2016-12
Published in: Stochastics and Dynamics, 16 (6), 1650014-1-1650014-17.
Document type: Article
Abstract: In this work we study the existence, uniqueness and asymptotic behavior of mild solutions for neutral stochastic partial integrodifferential equations with infinite delays. To prove the results, we use the theory of resolvent operators as developed by R. Grimmer [12] R. Grimmer. Resolvent operators for integral equations in a banach space. Transactions of the American Mathematical Society, 273(1): 333-349, 1982, as well as a version of the fixed point principle. We establish sufficient conditions ensuring that the mild solutions are exponentially stable in pth-moment. An example is provided to illustrate the abstract results.
Cite: Diop, M.A., Caraballo Garrido, T. y Zene, M.M. (2016). Existence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delays. Stochastics and Dynamics, 16 (6), 1650014-1-1650014-17.
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URI: http://hdl.handle.net/11441/52662

DOI: 10.1142/S0219493716500143

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