Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation
type: Item
instance of: scholarly article
title: Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation
zbMATH Open document ID: 1126.35061
author: Mónica Clapp
author: Tobias Weth
author: Thomas J. Bartsch
published in: Mathematische Annalen
publication date: 2007-06-07T00:00:00Z
review text: The authors establish lower bounds for the number of nodal bound states for the semiclassical nonlinear Schrödinger equation \(-\varepsilon ^{2}\Delta u+a\left( x\right) u=\left| u\right| ^{p-2}u\) in \({\mathbb R}^{N},\) with bounded and uniformly continuous potential \(a.\) The solutions have two nodal domains, and their positive and negative parts concentrate near the set of minimum points of \(a.\) The existence of infinitely many nodal solutions for fixed small \(\varepsilon \) is obtained. Variational techniques and Lusternik-Schnirelman theory are used. The paper provides the lower bounds for the cuplength of the configuration spaces.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 55R80
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5162074
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: critical point
zbMATH Keywords: configuration space
zbMATH Keywords: Lusternik-Schnirelman category
reviewed by: Radu Precup
MaRDI profile type: Publication
full work available at URL: s00208-006-0071-1
OpenAlex ID: W2070763546
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DOI: 10.1007/S00208-006-0071-1
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description: scientific article; zbMATH DE number 5162074