In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalize...

In this paper, the existence of fuzzy solutions for first and second order nonlocal impulsive neutral functional differential equations are studied using Banach fixed point theorem. We used the techniques of fuzzy set theory, functional analysis, and Hausdorff metric. Example is provide to illustrate the theory.

A periodical boundary value problem for a first-order system of ordinary integro-differential equations with impulsive effects and maxima is investigated. The obtained nonlinear functional-integral the existence uniqueness solution periodic are reduced to solvability equations. method successive approximations in combination compressing mapping used proof one-valued We define way aid which we c...

This paper introduces the concept of square-mean piecewise almost periodic for impulsive stochastic processes. The existence of square-mean piecewise almost periodic solutions for linear and nonlinear impulsive stochastic differential equations is established by using the theory of the semigroups of the operators and Schauder fixed point theorem. The stability of the square-mean piecewise almos...

Abstract It has become imperative in recent times to determine the properties of the solutions of certain mathematical equations or inequalities from the knowledge of associated inequalities or equations. In this paper, a number of oscillatory properties of the solutions of impulsive differential inequalities are established using the knowledge of those of their associated equations and what is...

This paper investigates the pth moment globally uniformly exponential stability of a class of impulsive stabilization of stochastic delay differential equations,and the pth moment exponential stability criteria is established by using theLyapunov–Razumikhin method. Keywords—Stochastic delay differential equations; Exponential stability ; Lyapunov-Razumikhin method ; Impulsive control

We investigate a delayed stage-structured Ivlev’s functional response predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that the behavior of impulsive stocking on prey plays an important role for the ...