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 Schr\"{o}dinger 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.

Keywords

• quasilinear schrödinger equation
• $l^\infty$-estimate
• asymptotically periodic
• nehari manifold