Asymptotic behavior of a class

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This paper is devoted to the existence and asymptotic behavior in p-th moment of the mild solution to a class of impulsive neutral stochastic functional integrodifferential equations with infinite delay in Hilbert spaces. A new and sufficient set of conditions are formulated concerning the existence of solutions and the stability of the nonlinear stochastic system. To obtain the desired result, the theory of the resolvent operator in the sense of Grimmer, the stochastic analysis theory, the fixed point theorem and the Hausdorff measure of non-compactness are used. However, it is very important to specify that in this paper, we have left the classical framework in which the nonlinear terms are assumed to be Lipschitz continuous. At the end of this paper, an illustration is also given to show the application of our results.
Stochastic differential equations have attracted great interest because of their applications in characterizing many problems in physics, mecanics, electrical engineering, biology, ecology and so on. On this matter, we refer the reader to [19, 20, 23] and references therein. In particular, integro-differential equations arise in the mathematical modeling of several natural phenomena and various investigations led to the exploration of their different aspects.
p-th moment stability, Neutral Impulsive Stochastic Functional Integrodifferential Equations, Infinite delay, Hausdorff measure of non-compactness, Darbo’s fixed point
Bete, H.K., Mane, A., Ogouyandjou, C., Diop, M.A. (2019). Asymptotic behavior of a class of impulsive partial stochastic functional neutral integrodifferential equations with infinite delay. Electronic Journal of Mathematical Analysis and Applications Vol. 7(1) Jan. 2019, pp. 176-201. ISSN: 2090-729X(online)