Nonlinear perturbations of a periodic Schrödinger equation with supercritical growth

Abstract

In this paper, we establish the existence of positive solutions for a class of quasilinear Schrodinger equations involving supercritical growth. By using a change of variables, the quasilinear equation is reduced to a semilinear equation. Then, variational method is used together with a truncation argument used in Del Pino and Felmer (Calc var Partial Differ Equ 4:121–137, 1996) and concentration compactness principle given in Zelati and Rabinowtiz (Commun Pure Appl Math 45:1217–1269, 1992.