A new index theory for linear self-adjoint operator equations and its applications
type: Item
instance of: scholarly article
title: A new index theory for linear self-adjoint operator equations and its applications
zbMATH Open document ID: 1334.58011
author: Qi Wang
author: Chungen Liu
published in: Journal of Differential Equations
publication date: 2015-12-18T00:00:00Z
review text: Consider a self-adjoint operator equation \[ Au=F'(u) \tag{OD} \] where \(H\) is an infinite-dimentional separable Hilbert space, \(A\) a self-adjoint operator on \(H\) with its domain \(D(A)\), \(F\) is a nonlinear functional on \(H\). In this paper, the authors develop a new index theory for \((OD)\) where the essential spectrum of the operator \(A\) may not be empty and they show that this index theory is a generalization of some other index theories. As applications, by assuming some twisted condition, they obtain the existence and multiplicity of periodic solutions for wave equations and beam equations.
reviewed by: Mohsen Timoumi
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 58J45
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 6522112
zbMATH Keywords: index theory
zbMATH Keywords: dual variational methods
zbMATH Keywords: wave equation
MaRDI profile type: Publication
full work available at URL: j.jde.2015.10.046
OpenAlex ID: W2177100767
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DOI: 10.1016/J.JDE.2015.10.046
description: scientific article; zbMATH DE number 6522112