| Integral inequalities provide a useful way to study ordinary differential equation and partial differential equation. Especially for the equations which are hard to find the clear solution. Integral inequalities play a great role in study of the nature of the solution. In recent years,the more focus on the retrded integral inequalities for discontinuous functions, the more scholars begin to discuss the Gronwall-Bellman type integral inequalities which have retarded cases and find lots of influential results.The purpose of this paper is tuo develop some of existing results, to get more new inequalities which have retarded cases.At the same time,we use the results of this paper to discuss some cases about solving impulsive inequalities.The thesis is divided into three sections according to contents.Chapter 1 This chapter develop the inequalities of literature[18]to common situation. We consider the nonlinear discrete integral inequalities.Chapter 2 In this chapter,to establish the following results with discontinuous functions.It is based on literature[19]. Besides,We discuss the results of the following inequalities when join in retarded cases, and study the application of the inequalities.Chapter 3 This chapter is based on literature[7]and research Gronwall-BellmanBihari type integral inequalities. |
