Multiplicity of periodic solutions of nonlinear wave equations.
type: Item
instance of: scholarly article
title: Multiplicity of periodic solutions of nonlinear wave equations.
zbMATH Open document ID: 1064.35119
author: Massimiliano Berti
author: Philippe Bolle
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-03-29T00:00:00Z
review text: The goal of the present paper is to complete the description of the small amplitude periodic solutions of (1) \[ u_{tt}-u_{xx}+f(u)=0\quad u(t,0)=u(t,\pi)=0,\tag{1} \] where \(f(0)=f'(0)=0\). To this end the authors prove ``optimal'' multiplicity results, finding the minimal periods of the solutions and showing their regularity. Here the authors use the variational Lyapunov-Schmidt reduction and minimax arguments.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 37K50
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 2062708
zbMATH Keywords: minimax arguments
zbMATH Keywords: infinite-dimensional Hamiltonian system
zbMATH Keywords: variational methods
zbMATH Keywords: Lyapunov-Schmidt reduction
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.na.2003.11.001
OpenAlex ID: W2137917876
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DOI: 10.1016/J.NA.2003.11.001
description: scientific article; zbMATH DE number 2062708