Study On The Existence Of Multiple Solutions Of Several Kinds Schr(?)dinger-Poisson Type Equations

In this paper,the existence of multiple solutions for several kinds of Schr(?)dinger-Poisson type equations is studied.By using the variational method,the corresponding results are established.Firstly,we consider the existence of high energy radial solutions for a class of following Schr(?)dinger-Poisson-Kirchhoff equations(?) where a>0,b>0,9/2<p<6.We use the fountain theorem to obtain the existence of high energy radial solutions for the Schr(?)dinger-Poisson-Kirchhoff equations.Secondly,we study the existence of infinitely many normalized radial solutions for the following quasilinear Schr(?)dinger-Poisson equations-△u-λu+(|x|-1*|u|2)u-△(u2)u-|u|p-2u=0,x ∈ R3,where p(10/3,6),λ∈R.Firstly,the quasilinear equations are transformed into a semilinear equation by making appropriate a change of variables,whose respective associated variational functional is well defined in Hr1(R3).Secondly,by constructing auxiliary functional and combining pohozaev identity,we prove that under constraints the energy functional related to the equation has a bounded Palais-Smale sequence on each level set.Finally,it is obtained that there are infinitely many normalized radial solutions for this kind of quasilinear Schr(?)dinger-Poisson equations.Lastly,we consider the existence of infinitely many solutions of Schr(?)dingerPoisson equations without any growth conditions:-△u-V(x)u+(|x|-1*u2)u-λu=f(u),x∈RN,where λ<0,V(x)∈ C[0,+∞)is a potential function and satisfies certain conditions.By using variational method,such as truncation function and Fountain Theorem,we get the existence of infinitely many solutions to revised equation.Then we use the Moser iteration to obtain the existence of infinitely many solutions to original Schr(?)dinger-Poisson equations.