The Existence Of Ground State Solutions And Positive Solutions For Two Classes Of Quasilinear Schr(?)dinger Equations

In this thesis,we are concerned with the existence of ground state solutions for quasilinear Schrodinger equation of Choquard type and the existence of positive solutions for p-Laplace type quasilinear Schrodinger equation with vanishing potentials by using the variational method.The main research content is stated as follows:The first part is devoted to studying the following quasilinear Schrodinger equation of Choquard type where N≥ 3,0<α<N,2<p<(N+α)/(N-2),κ>0,Iα is the Riesz potential,V(x)is a positive continuous potential.The existence of ground state solutions is established via Pohozaev manifold approach.The second part is to study the p-Laplace type quasilinear Schrodinger equations where N≥ 3,1<p<N,κ>0,V(x):RN→R is a nonnegative continuous function,which can vanish at infinity,f:R→R is a continuous function.The existence of positive solutions is established via mountain pass theorem and Moser iteration.