Existence of solutions for asymptotically periodic quasilinear Schrödinger equations with local nonlinearities

Abstract

This paper is concerned with the existence of positive solutions for asymptotically periodic quasilinear Schrödinger equations. By using a Nehari-type constraint and Moser iteration, we get the existence results which is a complement to the ones in Chu and Liu [Nonlinear Anal. Real World Appl. 44(2018), 118–127]. Moreover, we consider a new reformative asymptotic processes of the potential function and the nonlinearity term is only locally defined.