The Control of the Boundary Value Problem for Linear Impulsive Integro-Differential Systems

Abstract

Recently, there has been a lot of activity in the investigation of differential equations with solutions which undertake discontinuities or jumps at w x some definite instants 1]4 . At the same time, in the theory of impulsive differential equations there is a number of problems which are connected with the results of the theory of integral and integro-differential equations w x and which are not well investigated yet 3, 5]8 . The purpose of this paper is to consider a problem of finding conditions for controllability of the boundary value problem for a linear impulsive system of integro-differential equations. The problem of the control of the linear impulse system was w x considered in 9 . Moreover, the existence results and the integral representation of solutions of the second kind Volterra integro-summary equation and integro-differential equations are obtained with impulse actions at fixed moments of time. Necessary and sufficient conditions of the solvability of the boundary value problem for linear impulsive systems of integro-differential equations are defined. Q 1999 Academic Press