Studies On Some Nonlinear Discrete Inequalities And Their Applications

The purpose of this paper is to establish some new nonlinear discrete inequalities in two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used to investigate the qualitative theory of certain finite difference equations. In this paper we also established some new explicit bounds on solution to a class of new nonlinear Volterra-Fredholm-type discrete inequalities, which can be used as effective tools in the study of certain sum-difference equations. Application examples are also indicated.The thesis is divided into three sections according to contents.In Chapter 1, Preface, we introduce the main contents of this paper.In Chapter 2, we study the following discrete nonlinear inequalities and their applications.and We mainly improve some results of Meng [1]and obtained many good developments.In Chapter 3, we study some new nonlinear Volterra-Fredholm-type discreteinequalities and their applications. The forms are as follows:andEnlightened by Meng [1] and Meng [15], we studied the Volterra-Fredholm-typediscrete inequalities on infinite intervals.