Existence of ground state solutions for quasilinear Schrödinger equations with variable potentials and almost necessary nonlinearities

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. <i>Electronic Journal of Differential Equations, 2018</i>(157), pp. 1-13.

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Attribution 4.0 International

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