Several Class Inequality And Applications

It is widely recognized today, that the integral inequalities are of very impor-tant in the studying of stability, many other qualitative as well as quantitative properties of solution of differential equations. The well-known Gronwall inequal-itiy, Bihari inequality, Bellman inequality and their generalization have benn frequently employed in the studying of this direction. In recently years, many scholars take on the research of this field, they established some more general retarded integral inequalities from linear to nonlinear, and from one nonlinear to more nonlinear terms and so on,they have achieved many good results. Our main aim is to establish some new generalizations and extensions of these inequalities which can be used as handy tools in the study of certain new classes of ordinary differential equations and partial differential equations.The thesis is divided into three chapters.In Chapter 1, Preface, we introduce the main contents of this paper.In Chapter 2, we extend some new generalization of nonlinear Gronwall-Bellman-Ou-Iang integral inequalities which have two variables.In Chapter 3, The chapter investigates nonlinear integral inequalities. In 2009 Rui A.C.Ferreira and Delfim F.M.Torres established main inequalities as follows: and In this chapter, we mainly generalized above inequalities to two independent variables, and obtain some new integral inequalities, which can be used as tools in the theory of partial differential and integral equations.In Chapter 4,we will introduce several Ou-Iang integral inequalities which haveφ(t)=t2 in chapter 3.