Study On Infinitely High Energy Solutions And Ground State Solutions Of Schr(?)dinger-Poisson System

In this paper,the variational method is used to study the existence of the infinitely many high-energy solutions and ground state solutions of the Schr(?)dingerPoisson system When studying the infinite number of solutions of the system,we make the following assumptions about potential V.Firstly,V is mandatory,and there is a positive constant α such that the satisfaction V>α constant holds.Secondly V is differentiable and satisfies ▽V(x)·x∈Lr(R3).where the parameter r∈[3/2,+∞).Specifically,V satisfies the condition V(x)+▽V(x)·x≥ 0 is true almost everywhere.Assuming that the nonlinear term f satisfies some specific condition,through symmetric mountain pass theorem,We get an infinite number of solutions to the system(0.0.1).And then,we consider that in the system(0.0.1),take a special form for the nonlinear term on the right side of the system,and multiply a sufficiently large parameter λ in front of the steep potential V to obtain the following critical Schrodinger-Poisson system Here,V is steep geopotential and satisfies some other assumptions,and under some reasonable assumptions about g,using mountain pass theorem,the existence of the ground state solution of the unified(0.0.2)is obtained.