Open AccessAsymptotic stability of neutral stochastic functional integro-differential equations with impulses
Author(s) -
Mamadou Abdoul Diop,
Tomás Caraballo
Publication year - 2015
Publication title -
electronic communications in probability
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.236
H-Index - 38
ISSN - 1083-589X
DOI - 10.1214/ecp.v19-3036
Subject(s) - mathematics , lipschitz continuity , resolvent , nonlinear system , exponential stability , moment (physics) , mathematical analysis , fixed point theorem , stability (learning theory) , operator (biology) , biochemistry , chemistry , physics , classical mechanics , quantum mechanics , machine learning , repressor , computer science , transcription factor , gene
This paper is concerned with the existence and asymptotic stability in the \,p-th moment of mild solutions of nonlinear impulsive stochastic delay neutral partial functional integro-differential equations.
We suppose that the linear part possesses a resolvent operator in the sense given by Grimmer and the nonlinear terms are assumed to be Lipschitz continuous. A fixed point approach is used to achieve the required result. An example is provided to illustrate the theory developed in this work