Existence And Asymptotic Properties Of Solutions For Some Semilinear Elliptic Equations

In this paper,the main research content is the following equation,where the Ω?RN(N>3)is an open region,and it has a smooth boundary,0 ∈ Ω,the function b(x)is non-negative and continuous in Ω.Use the method of supersolution and subsolution,the principle of comparison,and other mathematical methods to study the properties of such equations,such as existence and asymptotic.The first part is the introduction.Firstly,the research background of semilinear elliptic differential equation and semilinear elliptic differential equation with Hardy term is introduced.Then the research conclusions of some scholars are given,and the main content and main conclusions of this paper are also briefly introduced.The space symbols used in this paper are described in the second chapter,and the lemma and definition cited in this paper are explained.In chapter 3,g(u)satisfies g(0)=0,(?),there is p>1,such that(?),in addition,g(u)satisfies the Keller-Osserman condition that where The upper and lower solutions of the equation are obtained by means of the method of upper and lower solutions and the comparison principle,and then it is concluded that the equation has the maximum positive solution and the minimum positive solution,and the asymptotic property near the origin is obtained.Chapter 4 explore a class of elliptic equations when g(u)=ueu,firstly,study the general term of this kind of blasting problem,g(u)=ueu,and then came to the conclusion that there is only one solution.The existence of the upper and lower solutions is obtained by using the correlation property of the inverse function and the definition of the upper and lower solutions.Furthermore,the blasting problem is studied and the uniqueness of the solution is obtained by using the principle of upper and lower solution.Finally,the existence of the solution in case g(u)-ueu is obtained by using this conclusion.The fifth chapter is the summary and prospect.The content of this paper is summarized and the future research is prospected.