Research On Existence Of Solutions For Several Classes Of Klein-Gordon-Maxwell Equations

The Klein-Gordon-Maxwell equation has a very broad physical background and plays an important role in both quantum field theory and relativistic quantum mechanics.Therefore,the existence of solu-tions for several classes of Klein-Gordon-Maxwell equations is studied in this paper.This paper consists of the following parts.The first chapter mainly describes the research background and status of Klein-Gordon-Maxwell equation.Chapter 2 lists definitions,theorems,lemmas,and inequalities that will be used.In the third chapter,the Klein-Gordon-Maxwell equation of the following form is studied by means of the variational method:The existence of nontrivial solutions of this equation is proved by using weaker conditions,which gener-alizes the results in the relevant literatures.In chapter 4,the existence of nontrivial solutions of Klein-Gordon-Maxwell equation of the following form is considered:By using the local super-quadratic conditions and some analytical techniques,some results for the exis-tence of nontrivial solutions of the equation are obtained,which generalize and improve the corresponding results in the literature.In chapter 5,we prove the existence of ground state solutions for three types of Klein-Gordon-Maxwell equations.Specifically,by using Pohozaev identity and the corresponding analytical techniques,we obtain the existence results of ground state solutions for two types of Klein-Gordon-Maxwell equations,which make the range of ? for the existence of solutions wider.Besides,we study the fractional Klein-Gordon-Maxwell equation.The sixth chapter summarizes the whole paper,points out the shortcomings in this paper,and gives the direction of the next research.