Nonlinear Retarded Integral Inequalities for Discontinuous Functions and its Applications

Abstract

AbstractIt is well-known that integral inequality for continuous function is an important tool for studying the existence, uniqueness, boundedness, stability and other qualitative properties of solutions of differential equations and integral equations. The integral inequality for discontinuous function is an important tool for studying impulsive differential equations as well. To study the estimations of solution of nonlinear retarded impulsive integral equation, firstly retarded integral inequalities including the nonlinear composite function of discontinuous function are established, next the estimations of the unknown function of the integral inequalities are given by the methods of replacement, enlargement, differential, integral, segmentation, mathematical induction. Finally, the estimations obtained here are used to give the estimation of the solution of a class of nonlinear impulsive differential equation.KeywordsRetarded integral inequalityDiscontinuous functionEstimation