The Positive Solutions To Elliptic System And The Roles Of Diferent History Functions

In this paper, we mainly studies the positive solutions to elliptic system and thediferent roles of history function in a type of autocatalytic models.The paper is divided into four chapters.The first chapter is the introduction of the whole paper. We talk about the back-ground of the problems and organize the structure of this paper.Some relevant definitions and basic theorems of elliptic system will be given in thesecond chapter. Using these tools, we will study the existence and multiplicity of thesolutionsIn the third chapter, we study a mathematical model of a chemical reaction. If weconsider the influence of the difusion,We focus on the roles of a type of history functionsH(u)=a+Bu for the properties of the solutions such as the stability of the equilibriumpoints and the existence of multiple solutions to the problem.We will sum up the conclusion of this paper in the fourth chapter.