Existence And Multiplicity Of Solutions For Two Classes Of Klein-Gordon-Maxwell Systems

In this paper,the existence and multiplicity of nontrivial solutions for two types of Klein-Gordon-Maxwell systems are studied via Variational methods and critical point theory.The article is organized as follows:The chapter 1 mainly introduces the research back-ground,research significance,and research status.The chapter 2 mainly introduces some properties of the Klein-Gordon-Maxwell system and some relevant abstract theorems.In chapter 3,a class of critical Klein-Gordon-Maxwell system with sublinear terms is studied.Under the condition that the potential function satisfies some integrability assumptions,firstly,a local minimal solution is obtained by using the Ekeland variational principle.Then,the existence of infinitely many negative energy solutions is obtained by using the dual foun-tain theorem.Finally,the existence of ground state solutions is also obtained.In chapter 4,a class of Klein-Gordon-Maxwell system with local sublinear terms is studied.The potential function is coercive and has a negative lower bound.The nonlinear term only satisfies some sublinear growth condition near zero.and no additive assumption is made at infinity.Firstly,since the nonlinear term does not have any growth condition at infinity,in order to apply variational methods,the original problem is converted into a variational problem by trun-cation techniques.Then.using a deformed Clark theorem,the existence of infinitely many negative energy solutions to this variational problem is obtained.Finally,by the theory of Elliptic regularity,the estimate of the solutions are obtained,then the solutions of the original problem are obtained.