EXISTENCE AND EXPONENTIAL STABILITY OF MILD SOLUTIONS FOR SECOND-ORDER NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION WITH RANDOM IMPULSES
Linxin Shu, Xiao‐Bao Shu, Quanxin Zhu, Fei Xu
Abstract
In this paper, we consider the existence and exponential stability in mean square of mild solutions to second-order neutral stochastic functional differential equations with random impulses in Hilbert space. Firstly, the existence of mild solutions to the equations is proved by using the noncompact measurement strategy and the Mönch fixed point theorem. Then, the mean square exponential stability for the mild solution of the considered equations is obtained by establishing an integral inequality. Finally, an example is given to illustrate our results.
Topics & Concepts
MathematicsMean squareExponential stabilityMathematical analysisHilbert spaceExponential functionStochastic differential equationFixed-point theoremDifferential equationApplied mathematicsStability (learning theory)Order (exchange)PhysicsFinanceComputer scienceMachine learningEconomicsQuantum mechanicsNonlinear systemNonlinear Differential Equations AnalysisStability and Controllability of Differential EquationsFractional Differential Equations Solutions