Some New Gronwall-Bellman-type Integral Inequalities With Multiple Independent Variables

Gronwall - Bellman inequality played an important role in the process of linear and nonlinear differential and integral equation theory development, for quite a long time, many scholars are committed to the research of Gronwall- Bellman inequal-ity, and functions contain a variable are generalized to functions in the form of two independent variables and multiple independent variables.In this paper, we establish some new Gronwall - Bellman Type Integral Inequal-ities of Several Independent Variables. The purpose of this paper is to extend the results proved in Zareen A. Khan [Int. Journal of Math. Analysis, Vol.6,2012,no.1,39-52]and Cheh - ChihYehAndMau - HsiangShih[Journal of Mathematical Analysis And Applications 86,157-167(1982)]. The inequalities theory of certain partial differ-ential equations.Based on the content, this paper is divided into the following three chapters:The first chapter:we mainly collect some basic definitions and facts that will be used in this article.The second chapter:The integral inequality in Zareen A. Khan [4]: Will be extended to form containing n variables: And then use the method in [4], the similar conclusions will be got.The third chapter:change the inequality of theorem 1 in Cheh-ChihY ehAndMau-HsiangShih [24]:And then use the method in [24], the similar conclusions will be got.