A nonlinear Schrödinger equation resonating at an essential spectrum
type: Item
instance of: scholarly article
title: A nonlinear Schrödinger equation resonating at an essential spectrum
zbMATH Open document ID: 1406.35346
DOI: 10.1155/2016/3042493
author: Shaowei Chen
author: Haijun Zhou
published in: Advances in Mathematical Physics
publication date: 2018-10-17T00:00:00Z
review text: Summary: We consider the nonlinear Schrödinger equation \(-\Delta u + f(u) = V(x) u\) in \(\mathbb{R}^N\). The potential function \(V\) satisfies that the essential spectrum of the Schrödinger operator \(-\Delta - V\) is \([0, + \infty)\) and this Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. The nonlinearity \(f\) satisfies the resonance type condition \(\operatorname{\lim}_{\left|t\right| \rightarrow \infty} f(t) / t = 0\). Under some additional conditions on \(V\) and \(f\), we prove that this equation has infinitely many solutions.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35B34
Mathematics Subject Classification ID: 35P30
zbMATH DE Number: 6957367
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: infinitely many negative eigenvalues
MaRDI profile type: Publication
Wikidata QID: Q59122209
full work available at URL: https://doi.org/10.1155/2016/3042493
OpenAlex ID: W2290297985
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description: scientific article; zbMATH DE number 6957367