Existence of ground state solutions for quasilinear Schrödinger equations with variable potentials and almost necessary nonlinearities
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Date
2018-08-29
Authors
Chen, Sitong
Tang, Xianhua
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we prove the existence of ground state solutions for the quasilinear Schrödinger equation
-∆u + V(x)u - ∆(u2)u = g(u), x ∈ ℝN,
where N ≥ 3, V ∈ C1(ℝN, [0, ∞)) satisfies mild decay conditions and g ∈ C(ℝ, ℝ) satisfies Berestycki-Lions conditions which are almost necessary. In particular, we introduce some new inequalities and techniques to overcome the lack of compactness.
Description
Keywords
Quasilinear Schrödinger equation, Ground state solution, Berestycki-Lions conditions
Citation
Chen, S., & Tang, X. (2018). Existence of ground state solutions for quasilinear Schrödinger equations with variable potentials and almost necessary nonlinearities. Electronic Journal of Differential Equations, 2018(157), pp. 1-13.
Rights
Attribution 4.0 International