Existence and stability of mild solutions to non autonomous impulsive stochastic neutral integrodifferential equations

Thiam, P. A.¹ ; Elbou, Kh.² ; Abdi, S. A.² ; Diop, M. A.³

¹ UFR SAT Département de Mathématiques, Université Gaston Berger de Saint-Louis, B.P234, Saint-Louis, Sénégal
² Département de Mathématiques et Informatique, Université de Nouakchot A-Lasriya, Mauritania
³ UFR SAT Département de Mathématiques, Université Gaston Berger de Saint-Louis, B.P234, Saint-Louis, Sénégal;c-UMMISCO UMI 209 IRD/UPMC, Bondy, France

Journal of nonlinear sciences and its applications, Tome 17 (2024) no. 4, p. 191-207.

Résumé

‎The research presented in this article focuses on studying a specific category of impulsive stochastic neutral integrodifferential systems in real Hilbert space‎. ‎The first step in this process is to derive sufficient conditions for the existence and uniqueness of a mild solutions‎. ‎We obtain our results using Banach's fixed point theorem and various techniques from stochastic analysis‎. ‎In addition‎, ‎an investigation of the exponential $p$-stability of the mild solutions is carried out‎. ‎For an illustration of how our findings can be used‎, ‎see the final section of this paper‎.

Détail

DOI : 10.22436/jnsa.017.04.03

Classification : 47G20, 47A10, 49J30, 60G22, 03C45
Keywords: Neutral stochastic integro-differential equations, resolvent operator, mild solution, standard Brownian motion, exponential stability

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