On periodic solutions of the nonlinear suspension bridge equation
type: Item
instance of: scholarly article
title: On periodic solutions of the nonlinear suspension bridge equation
zbMATH Open document ID: 0733.35104
author: Q-Heung Choi
author: Tacksun Jung
published in: Differential and Integral Equations
publication date: 1991-01-01T00:00:00Z
review text: This paper is devoted to the study of the nonlinear oscillations of \[ - Ku_{xxtt}+u_{tt}+u_{xxxx}+bu^+=1+k \cos x+h(x,t), \] assuming that u and \(u_{xx}\) vanish for \(x=\pm \pi /2\), \(t>0\). The main results deal with the special cases \(K=1/4\), \(b\in (4,19)\) and \(K=0\), \(b=b(x)\). Existence, uniqueness, and nonuniqueness theorems are given. The treatment is very elegant. Moreover, there seem to be a number of natural, open questions associated with this equation.
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 35G30
zbMATH DE Number: 4212653
zbMATH Keywords: nonlinear suspension bridge equation
zbMATH Keywords: oscillations
zbMATH Keywords: Existence
zbMATH Keywords: uniqueness
zbMATH Keywords: nonuniqueness
reviewed by: Ronald B. Guenther
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4212653