Solutions for a quasilinear Schrödinger equation: a dual approach.
type: Item
instance of: scholarly article
title: Solutions for a quasilinear Schrödinger equation: a dual approach.
zbMATH Open document ID: 1035.35038
author: Mathieu Colin
author: Louis Jeanjean
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-03-14T00:00:00Z
review text: The authors develop a variational approach in \(H^1(\mathbb{R}^N)\) for proving the existence of solutions of a quasilinear stationary Schrödinger equation. This is achieved by means of a suitable change of variables for transforming the problem into an equation of a semilinear elliptic type to which one applies the Mountain Pass geometry.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 2056121
zbMATH Keywords: quasilinear Schrödinger equation
zbMATH Keywords: minimax methods
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
full work available at URL: j.na.2003.09.008
OpenAlex ID: W143622551
cites work: Q3333435
cites work: Nonlinear scalar field equations. I: Existence of a ground state
cites work: Electron self-trapping in a discrete two-dimensional lattice
cites work: Stability of stationary waves for a quasilinear Schrödinger equation in space dimension 2.
cites work: Homoclinic type solutions for a semilinear elliptic PDE on ℝn
cites work: Q4692985
cites work: Soliton solutions for quasilinear Schrödinger equations, I
cites work: Soliton solutions for quasilinear Schrödinger equations. II.
cites work: A remark on least energy solutions in $\mathbf {R}^N$
cites work: A Note on a Mountain Pass Characterization of Least Energy Solutions
cites work: The concentration-compactness principle in the calculus of variations. The locally compact case. II
cites work: On the existence of soliton solutions to quasilinear Schrödinger equations
DOI: 10.1016/J.NA.2003.09.008
description: scientific article; zbMATH DE number 2056121