Study On The Existence And Asymptotic Behavior Of Solutions For Klein-Gordon-Maxwell System

Klein-Gordon-Maxwell system has a profound physical background,and the study of this mathematical model is of great significance both in theory and in practice.In this paper,the existence of solutions of Klein-Gordon-Maxwell system in different forms and conditions is studied by using variational method and critical point theory by making appropriate assumptions about potential function and nonlinear term,or adding parameters.The full text consists of five chapters,and the specific arrangements are as follows:In Chapter 1,we introduce the research background,research results and progress of Klein-Gordon-Maxwell system,and expounds the main research contents and related preparatory knowledge of this paper.In Chapter 2,the mountain pass theorem and truncation technique are used to study the nonlinear Klein-Gordon-Maxwell system with steep potential well and the existence and asymptotic behavior of nontrivial solutions when the nonlinear term of the system is f（x,u）:= |u|^q-2u,where 2 < q < 4.In Chapter 3,the existence of infinite small energy solutions for Klein-GordonMaxwell system is proved by using symmetric mountain pass theorem and Moser iteration method under the condition that the nonlinear term satisfies local superquadratic growth.In Chapter 4,the existence of nontrivial solutions for a special Klein-GordonMaxwell system is obtained by using truncation discussion,mountain pass theorem and L^∞estimation.In Chapter 5,the main research results of this paper are briefly summarized,and some problems worthy of further discussion in the future are put forward.