On a periodic Schrödinger equation involving periodic and nonperiodic nonlinearities in \(\mathbb{R}^2\)
type: Item
instance of: scholarly article
title: On a periodic Schrödinger equation involving periodic and nonperiodic nonlinearities in \(\mathbb{R}^2\)
zbMATH Open document ID: 1401.35113
author: Marcius Cavalcante
author: Claudianor O. Alves
author: Everaldo S. Medeiros
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-05-31T00:00:00Z
review text: This paper deals with a Schrödinger-type equation involving periodic and nonperiodic nonlinearities in the two-dimensional Euclidean space. The problem also contains a potential \(V\) that is 1-periodic and such that 0 lies in a spectral gap of the spectrum of the linear Schrödinger l operator \(-\Delta + V\). The reaction has exponential growth in the sense of Trudinger-Moser. The nonlinear term is allowed to be both periodic and nonperiodic in the spatial variable. The proofs combine the linking theorem and the Lions concentration-compactness principle.
reviewed by: Teodora-Liliana Rădulescu
Mathematics Subject Classification ID: 35J91
zbMATH DE Number: 6877120
zbMATH Keywords: linear Schrödinger operator
zbMATH Keywords: semilinear equation
zbMATH Keywords: periodic potential
zbMATH Keywords: spectral theory
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.01.053
OpenAlex ID: W2791837451
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DOI: 10.1016/J.JMAA.2018.01.053
description: scientific article; zbMATH DE number 6877120