The Existence Of Ground State Solutions For A Class Of Equations Related To Klein-Gordon-Maxwell Systems

In this paper,we will study the existence of ground state solutions for a class of nonlinear equations by using the theory of compactness of concentration,variational method and critical point theory.(?) where u∈H~1(R~3),Q∈H~1(R~3),λ>0,m and ω are positive constants.Then we study the problem assuming the follwwing two cases on A(x).If A(x)is a positive constant function,we prove that the ground state solution(u,φ)exists for any p ∈(3,6);If A(x)is not a constant function,we prove that the ground state solution(u,φ)exists for any p ∈(4,6)under the right conditions.