Existence and stability results for a partial impulsive stochastic integro-differential equation with infinite delay

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• 作者：Mamadou Abdoul Diop ; Khalil Ezzinbi ; Mahamat Mahamat Zene
• 关键词：Resolvent operators ; \(C_0\) ; semigroup ; Neutral stochastic partial integrodifferential equations ; Wiener process ; Picard iteration ; Mild solutions ; Stability in mean square
• 刊名：SeMA Journal
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：73
• 期：1
• 页码：17-30
• 全文大小：462 KB
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• 作者单位：Mamadou Abdoul Diop (1)
  Khalil Ezzinbi (2)
  Mahamat Mahamat Zene (1)
  
  1. UFR SAT Département de Mathématiques, Université Gaston Berger de Saint-Louis, B.P 234, Saint-Louis, Senegal
  2. Département de Mathématiques, Université Cadi Ayyad Faculté des Sciences Semlalia, B.P. 2390, Marrakech, Morocco
  
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Milan
• ISSN：2254-3902

文摘

This article presents the result on existence and stability of mild solutions of stochastic partial differential equations with infinite delay in the phase space \(\mathcal {B}\) with non-lipschitz coefficients.  We use the theory of resolvent operator devolopped in Grimmer (Trans Am Math Soc 273(1):333–349, 1982) to show the existence of mild solutions. An example is provided to illustrate the results of this work.