The study of impulsive functional differential equations is linked to their utility in simulating processes and phenomena subject to short-time perturbations during their evolution. The perturbations are performed discretely and their duration is negligible in comparison with the total duration of the processes. That is why the perturbations are considered to take place “instantaneously” in the...

Impulsive differential equations, which arise in biology, physics, population dynamics, economics, etc., are a basic tool to study evolution processes that are subjected to abrupt in their states (see [8-12]). Recently, the existence results were extended to anti-periodic boundary value problems for first-order impulsive differential equations [13,14]. Very recently, Wang and Shen [15] investig...

This paper is concerned with the existence of mild solutions of some classes of initial value problem for firstand second-order impulsive semilinear functional and neutral functional differential equations. Initially, we will consider initial value problems for firstorder impulsive semilinear functional differential equations y′(t)−Ay(t) = f (t, yt), a.e. t ∈ J := [0,b], t = tk, k = 1, . . . ,m...

This paper concerned with the existence of solutions of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator. Firstly, the definition a pair of coupled lower and upper solutions of the problem is introduced. Then, under the approach of coupled upper and lower solutions together with Nagumo condition, we prove that there exists at least one solutio...

This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and twostep BDFmethod are of order p 0when applied to impulsive differential equations. An improved linear multistep method is proposed. Convergence and stability conditions of the improved methods are given in the p...

Asymptotic equilibria of linear integro-differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro-differential equations are established. A new Gronwall–Bellman type lemma for integro-differential inequalities is proved. An example is given to demonstrate the validity of one of the results. c © 2008 Elsev...