Multiple solutions for some nonlinear Schrödinger equations with indefinite linear part
type: Item
instance of: scholarly article
title: Multiple solutions for some nonlinear Schrödinger equations with indefinite linear part
zbMATH Open document ID: 1123.35073
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-04-26T00:00:00Z
review text: The author considers a class of nonlinear Schrödinger equations with indefinite linear part in \(\mathbb{R}^N\): \(-\Delta u+V_\lambda (x) u=f(x,u),\;u\in H^1(\mathbb{R}^N).\) It is proved that the corresponding problem has at least three nontrivial solutions. The results are primarily an application of a linking theorem, due to \textit{M. Willem} [Minimax Theorems, Birkhäuser Boston (1996; Zbl 0856.49001)], and a (\(\nabla\))-Theorem, initiated by \textit{A. Marino} and \textit{C. Saccon} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 25, No.~3--4, 631--665 (1997; Zbl 1033.35026)]).
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5146723
zbMATH Keywords: linking theorem
zbMATH Keywords: (\(\nabla\))-theorem
zbMATH Keywords: orthogonalization technique
author: Feizhi Wang
reviewed by: Wen-Xiu Ma
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.09.047
OpenAlex ID: W1990231253
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DOI: 10.1016/J.JMAA.2006.09.047
description: scientific article; zbMATH DE number 5146723