Nonlinear perturbations of a periodic Schrödinger equation with supercritical growth
type: Item
instance of: scholarly article
title: Nonlinear perturbations of a periodic Schrödinger equation with supercritical growth
zbMATH Open document ID: 1339.35126
author: Giovany M. Figueiredo
author: Sandra Im. Moreira
author: Olimpio H. Miyagaki
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2015-11-24T00:00:00Z
review text: The main focus in the paper under review is on the study of the existence of positive solutions for the quasilinear elliptic problem \[ -\Delta u - \Delta(u^2)u +V(x) u=p(u),\quad x\in\mathbb{R}^N, \quad N\geq 3, \] where \(V:\mathbb{R}^N\to \mathbb{R}\) is a continuos function positive function and \(p:\mathbb{R}\to \mathbb{R}\) has the form \(p=f_0 + \varepsilon g\). Moreover, both functions \(V\) and \(p\) satisfy certain additional assumptions. As their main result, the authors establish the existence of a positive solution for all sufficiently small values of a positive parameter \(\varepsilon\) in two cases: (i) \(V\) is a periodic function, and (ii) \(V\) is a small perturbation of a periodic potential.
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 6513335
zbMATH Keywords: quasilinear Schrödinger equations
zbMATH Keywords: variational methods
zbMATH Keywords: supercritical exponent
reviewed by: Aleksey Kostenko
MaRDI profile type: Publication
full work available at URL: s00033-015-0525-y
OpenAlex ID: W2075290099
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DOI: 10.1007/S00033-015-0525-Y
description: scientific article; zbMATH DE number 6513335