Existence and nonexistence results for quasilinear Schrödinger equations with a general nonlinear term
Volume 120 / 2017
Annales Polonici Mathematici 120 (2017), 271-293
MSC: 35J20, 35J62, 35B09.
DOI: 10.4064/ap170502-2-12
Published online: 20 December 2017
Abstract
We study the quasilinear Schrödinger equation $$ -\varDelta u+V(x)u-\varDelta (u^2)u=g(u), \hskip 1em\ x\in \mathbb {R}^N, $$ where $V(x)$ tends to zero as $|x|\rightarrow \infty $ and $g(u)$ satisfies the general hypotheses introduced by Berestycki and Lions. We employ the mountain pass theorem to obtain the existence of a positive ground state solution. Moreover, we prove a nonexistence result by using the Pohozaev manifold.
