Existence Of Solutions For Two Kinds Of Klein-Gordon-Maxwell Type Systems

First consider a Klein-Gordon-Maxwell type system with a steep potential well and a critical exponential term,Where ω>0 is a constant,u,φ:R3→R,in the non-linear term f(x,u)satis-fies a certain condition.Under the conditions,using the variation method such as Mountain Road Lemma and some analysis techniques,we obtain the existence of the ground state solution of the system and do a centralized analysis of the ground state solution.Secondly,study a kind of Klein-Gordon-Maxwell type system with forced po-tential as followsWhere ω>0 is a constant,u,φ:R3→R,in the non-linear term f(x,u)satis-fies a certain condition.Under the conditions,using Dual fountain theorem and some analysis techniques,we obtain the existence of infinitely many solutions of the system.This article is divided into four chapters.The first chapter is an introduction and literature review.It mainly discusses the background and significance of the topic,the current status and main results of the problem research,and some symbolic explanations.The second chapter studies the first category Klein-Gordon-Maxwell System,get the existence of ground state solutions,and do a centralized analysis of the ground state solution;Chapter 3 studies the second type Klein-Gordon-Maxwell system and obtains the existence of infinite solutions;Chapter 4 deals with problems Some reflections and outlooks.