Application of local linking to asymptotically linear wave equations with resonance
type: Item
instance of: scholarly article
title: Application of local linking to asymptotically linear wave equations with resonance
zbMATH Open document ID: 1109.58020
author: Shizuo Miyajima
author: Mieko Tanaka
published in: Tokyo Journal of Mathematics
publication date: 2006-12-12T00:00:00Z
review text: The authors provide a proof of the existence of a nontrivial time-periodic solution to the following nonlinear wave equation (WE) with asymptotically linear nonlinear term \(h(\square:=\partial^2/\partial t^2-\partial^2/\partial x^2)\): \[ \begin{cases} \square u(x,t)=h\bigl(x,t,u(x,t)\bigr), \quad & (0<x<\pi,\;t\in\mathbb{R}),\\ u(0,t)=u(\pi,t)=0\quad & (t\in\mathbb{R}),\\ u(x,t+2\pi)=u(x,t)\quad & (0<x<\pi,\;t\in\mathbb{R})\end{cases}.\tag{WE} \] This is a well written paper with interesting results.
reviewed by: Themistocles M. Rassias
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L35
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 5079799
zbMATH Keywords: variational method
zbMATH Keywords: super-linear
zbMATH Keywords: Lipschitz continuous
zbMATH Keywords: pseudo-gradient flow
zbMATH Keywords: vector field
zbMATH Keywords: homotopy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1166661865
OpenAlex ID: W2004153626
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DOI: 10.3836/TJM/1166661865
description: scientific article; zbMATH DE number 5079799