The Ground State Solution And Sign-changing Solution Of The Schrodinger-Poisson Equation

In this paper,we mainly consider the on ground state and nodal solutions of Schr?ding er-Poisson equations with different critical nonlinearity.Firstly,we consider the following Schr?dinger-Poisson system:(?),where ? is a parameters,and q?(2,5).Under some certain assumptions on V(x),K(x),and a(x),we prove that for every?>0 and q?(2,5),the Schr?dinger-Poisson equation with critical growth has at least a positive ground state solution by Mountain pass theorem in chapter two.Secondly,We consider another Schr?dinger-Poisson equation with different critical nonlinearity (?),where p?(4,6).We make some different assumptions on V(x),K(x),and a(x),we prove the existence of the ground state solution and nodal solution for Schr?dinger-Poisson equation with critical growth by Mountain pass theorem and a new method in chapter three.