Nontrivial And Ground State Soluion For The Quaslinear Schr(?)dinger-Poisson System With Convolution Type

In this thesis,we are concerned with the following quasilinear Schr(?)dinger-Poisson system with Choquard type:where 4+α≤p<6+2α,V∈ C(R3,R)and Iα:R3 →R is the Riesz potential.In chapter 1,the first part we introduce the research progress of the quasilinear Schrodinger equarion,Choquard equation,Schrodinger-Poisson system,and the second part introduce the main content of this paper.We get the energy functional of the above equations as follows:Due to the existence of ∫R3 u2|(?)u|2,J(u)is not defined on H1(R3).We solve this problem by replacing u=f(v)with a variable and introduce the related properties.In chapter 2,we introduce the relevant notions,definition and lemmas in this paper.In chapter 3,when α∈E(0,3)and the potential function V(x)satisfies the following assumptions:(V1)in fR3V(x)=V0>0;(V2)V(x)≤V∞=lim|y|→∞V(y)<∞ and Vo<V∞.we prove the existence of nontrivial solutions of the above equations by the Mountain pass theorem and reduction method.In chapter 4,when α∈ E(2,3)and the potential function V(x)satisfies the following assumptions:(V3)V∈ C1(R3);(V4)V(x)=V(|x|)and there exists 0<a ≤b such that a ≤V(x)≤ b;(V5)there exists a constant θ∈(0,1)and L≥ 0 such that we establish the existence of the ground state solution of the above equation set by L.Jeanjean theorem.