Existence of ground state solutions for generalized quasilinear Schr\”{o}dinger equations with asymptotically periodic potential

Abstract

This article is concerned with the existence of positive ground state solutions for an asymptotically periodic quasilinear Schr\”{o}dinger equation. By using a Nehari-type constraint, we get the existence results which improve the ones in Shi and Chen [Comput. Math. Appl. 71, 2016, 849-858]. Moreover, we give an application of our results, which extends the results in Li [Commun. Pure Appl. Anal. 14, 2015, 1803-1816].