Bifurcation into spectral gaps
type: Item
instance of: scholarly article
title: Bifurcation into spectral gaps
zbMATH Open document ID: 0864.47037
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1996-02-07T00:00:00Z
review text: The author gives a unified treatment and some refinements of recent results on the existence and bifurcation of non-trivial solutions of equations having the form \(Su-R(u)= \lambda u\), where \(S\) is an unbounded selfadjoint operator in a real Hilbert space, \(R\) is a potential operator with \(R(u)= o(u)\) for \(u\) near 0 and \(\lambda\not\in \sigma(S)\). The approach is a variational one and is based on the study of an associated equation of the form \((A-\lambda L)u- N(u)=0\), where \(A\) and \(L\) are bounded selfadjoint operators on a Hilbert space \(H\), \(N\in C^1(H,H)\), \(N(0)=0\) and \(N'(0)=0\). Applications are given to bound states for nonlinear Schrödinger equations and homoclinic solutions of Hamiltonian systems.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 58E07
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 833466
zbMATH Keywords: spectral gaps
zbMATH Keywords: existence
zbMATH Keywords: bifurcation
zbMATH Keywords: unbounded selfadjoint operator
zbMATH Keywords: real Hilbert space
zbMATH Keywords: bounded selfadjoint operators
zbMATH Keywords: bound states
zbMATH Keywords: nonlinear Schrödinger equations
zbMATH Keywords: homoclinic solutions
zbMATH Keywords: Hamiltonian systems
author: C. A. Stuart
reviewed by: Radu Precup
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 833466