Asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with \(H^{1}\)-supercritical exponent
type: Item
instance of: scholarly article
title: Asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with \(H^{1}\)-supercritical exponent
zbMATH Open document ID: 1333.35070
author: Shinji Adachi
author: Tatsuya Watanabe
published in: Journal of Differential Equations
publication date: 2015-12-07T00:00:00Z
review text: This paper is concerned with the study of entire solutions of the nonlinear Schrödinger-type equation \[ -\Delta u+\lambda u-\kappa \Delta (|u|^\alpha)|u|^{\alpha -2}u=|u|^{p-1}u,\quad x\in {\mathbb R}^N \;(N\geq 3), \] where \(\alpha, p\in (1,\infty)\) and \(\lambda,\, \kappa\) are positive parameters. The first main result in this paper is concerned with the uniqueness and the non-degeneracy of the related zero mass problem. This property is useful in order to obtain the asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with \(H^1\)-supercritical exponent. The proofs combine a dual variational approach with ODE techniques.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B08
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 6517096
zbMATH Keywords: quasilinear elliptic equation
zbMATH Keywords: asymptotic uniqueness
zbMATH Keywords: zero mass case
MaRDI profile type: Publication
full work available at URL: j.jde.2015.10.029
OpenAlex ID: W1902603562
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DOI: 10.1016/J.JDE.2015.10.029
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description: scientific article; zbMATH DE number 6517096