This paper investigates impulsive stabilization of stochastic delay differential equations. Both moment and almost sure exponential stability criteria are established using the Lyapunov–Razumikhinmethod. It is shown that an unstable stochastic delay system can be successfully stabilized by impulses. The results can be easily applied to stochastic systems with arbitrarily large delays. An exampl...

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and Applied Analysis 3 Note that V(t∗) = Q(t∗) + C 2 ‖Φ‖ τ e ∫ t ∗

K e y w o r d s I m p u l s i v e functional differential equations, Variable times, Fixed point. 1. I N T R O D U C T I O N This note is concerned with the existence of solutions, for the initial value problems (IVP for short), for first-order functional differential equations with impulsive effects y' ( t )=f( t , yt), a.e. t e J = [ O , T ] , t¢Tk(y(t)), k = l , . . . , m , (1) y(t +) = Ik(y...

The notion of Lipschitz stability of impulsive systems of differential equations (DEs) was introduced. In this paper, we will extend the notion of eventual stability to impulsive systems of DEs and extend the notion of Lipschitz stability of impulsive systems of DEs to a new type of stability called eventual Lipschitz stability. Some criteria and results are given. Our technique depends on Liap...

In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.

This paper is devoted to study the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Mönch’s fixed point theorem and the technique of measures of noncompactness.

The paper is concerned with stabilization of a scalar delay differention equation ẋ(t)− m ∑ k=1 Ak(t)x[hk(t)] = 0, t ≥ 0, x(ξ) = φ(ξ), ξ < 0, by introducing impulses in certain moments of time x(τj) = Bjx(τj − 0), j = 1, 2, . . . . Explicit stability results are presented both for the equation with positive coefficients and for the equation with Ak being of arbitrary sign. Supported by Israel M...

The cone theory andmonotone iterative technique are used to investigate theminimal nonnegative solution of nonlocal boundary value problems for second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times. All the existing results obtained in previous papers on nonlocal boundary value problems are under the case of the boundary condi...