Multiple solutions for a class of quasilinear Schrodinger equations in R-N

摘要

In this work, we study the existence of multiple solutions to a class of quasilinear Schrodinger equation - Delta(p)u + V(x)vertical bar u vertical bar(p-2)u - Delta(p)(vertical bar u vertical bar(2 alpha))vertical bar u vertical bar(2 alpha-2)u = g(u), x is an element of R-N, where Delta(p)u = div(vertical bar del u vertical bar(p-2)del u) is the p-Laplacian operator and p is an element of[2 alpha, N], alpha > 1/2 is a parameter. The potential V is an element of C(R-N) is positive and bounded in R-N. g(u) is odd and continuous. Using symmetric mountain pass lemma, we obtain infinitely many solutions to Schrodinger equation. (C) 2015 AIP Publishing LLC.