Ground state solutions for quasilinear Schr\”{o}dinger equations with critical Berestycki-Lions nonlinearities

Abstract

We consider the quasilinear Schr\”{o}dinger equation involving a general nonlinearity at critical growth. By using Jeanjean’s monotonicity trick and the Pohozaev identity, we get the existence results which generalize an earlier work (Liu and Zhao, Commun. Pure Appl. Anal. 19: 3429-3444, 2020) about the subcritical case to the critical case.