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 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.
