Existence And Multiplicity Of Solutions For Two Classes Of Nonlinear Elliptic Equations

This paper mainly studies two kinds of nonlinear variational problems.Firstly,we study the existence and multiplicity result for the Schr(?)dinger-Poisson equations(?)without compactness condition.Under suitable conditions,by using cut-off technique,Pohozaev type identity and variational method,we get existence and multiplicity result to(P).Secondly,we consider the following Kirchhoff problem(?)which is different from usual Kirchhoff type problem.We obtain that(K)possesses at least a nontrivial solution,a nontrivial non-negative solution and a nontrivial non-positive solution.Furthermore,we prove that the problem possesses one least energy sign-changing solution for the first time.