Study On The Solutions To A Class Of Quasilinear Schrodinger Equations

In this paper,we study the existence of solutions for quasilinear elliptic equations involving p-Laplacian-Δpu+V(x)|u|p-2u-Δp(|u|2)u=|u|q-2u,x∈RN,where 1<p<N,N≥3 and the function V(x)is periodic in each variable of x1,…,xN.If 2p<q<2p*(p*=Np/N-p),then we obtain a nontrivial solution of the above equation by Mountain Pass Lemma and Lions lemma;if q≥2p*and V(x)is positive constant,then we prove that the equation has no nontrivial solution by the Pohozaev identity.