Explicit Bounds On Solutions Of Some Retarded Integral Inequalities And Their Applications

Integral inequalities play a fundamental role in the development of the theory of differential equations and their applications. Recently, many such new inequalities have been discovered, and the study on explicit bounds on various retarded integral inequalities equations receives much attention of researchers. Seeking new tools and methods is still our urgent duty.In this thesis, by means of the Ou-Iang integral inequality, some new retarded integral inequalities are established and the explicit bounds on their unknown solutions are derived. Their applications to some nonlinear differential and integral equations are discussed. The obtained results improve and generalize some known results derived in the literature.This thesis includes three chapters. The first chapter establishes some new nonlinear retarded integral inequalities in n independent variables, which generalize some knowninequalities. In the second chapter, lettingω(t) be nonnegative continuous functionforω(t) > 0 (t> 0), explicit bounds on solutions of some new and more general inequalities are derived, which can be applied to ensure the boundedness of solution to certain integral equation with time delay. By replacing the nonnegative constant c with the function of x and y, the third chapter derives some new retarded integral inequalities in two independent variables.