Solutions Of Two Types Of Elliptic Equations With Critical Nonlinear Terms

In this paper,we mainly consider two equations.Firstly,we consider the following Kirchhoff type equation on the whole space (?) where?>0 is a real number,a,b>0,k and g satisfy some conditions.We mainly investigate the existence of at least one ground state solution via variational method and concentration-compactness principle.Secondly,we consider the following Schdr(?)inger-Poisson equation (?) where?is a bounded smooth domain in R~3,?>0 and the nonlinear growth of u~5reaches the Sobolev critical exponent in three spatial dimensions.With the aid of variational methods and the concentration compactness principle,we prove the problem admits at least two positive solutions and one positive ground state solution.