This paper regards initial value problem for second order impulsive integro-differential equations as some nonlinear vector system. By means of the Mönch′s fixed point theorem, some existence theorems of solutions of the initial value problem are established. The results are newer than all of the previous ones because of the more general form compactness-type condition and the weaker restrictio...

The main purpose of the paper is to summarize some fundamental results concerning the matrix impulsive differential equations with impulses at fixed points. The theory of impulsive matrix differential equations is interesting in itself and it will assume greater importance in the near future, since the application of the theory to various fields of science is also increasing, especially in the ...

We study the stability of the zero solution of an impulsive set differential system with delay by means of the perturbing Lyapunov function method. Sufficient conditions for the stability of the zero solution of impulsive set differential equations with delay are presented.

Partial averaging for impulsive differential equations with supremum is justified. The proposed averaging schemes allow one to simplify considerably the equations considered.

In this paper, we devote to investigation of even order impulsive delay differential equations, new oscillation criteria for every solution of equations are established.

The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of singular differential equations and singular impu...