Research On Some New Integrals Inequalities

Differential equation, integral equation and difference equation have played exten-sive applications, mainly be used in mathematical, physical, medical, optical, power system, etc. So many scholars began to study them in various fields. Among them,Gronwall inequality and Wendroff integral inequalities and their weakly singular inte-gral inequalities have played important roles in the research on Properties of differential equations. In this paper, we will build some new inequalities and apply the results to study uniqueness, boundedness, and continuous dependence of solutions of differential equations.In this paper, based on references [13, 14, 15, 24, 30], the related integral inequal-ities are generalized, and some new results are obtained.This paper is divided into the following four chapters:Chapter 1 The introduction. we will introduce the main problems and the back-ground of this paper.Chapter 2 According to some known integral inequalities in reference [15], the following results will be studied:Chapter 3 Some new Wendroff-type inequalities are studied and generalized to the following integral inequality with two variables:Chapter 4 The following Henry-type weak singular integral inequalities are studied:...