Blow up oscillating solutions to some nonlinear fourth order differential equations
type: Item
instance of: scholarly article
title: Blow up oscillating solutions to some nonlinear fourth order differential equations
zbMATH Open document ID: 1237.34043
author: Raffaella Pavani
author: Filippo Gazzola
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2011-10-17T00:00:00Z
review text: The authors consider the following non-linear differential equation: \[ w^{(4)}(s) + k{w}''(s) + f(w(s)) = 0, \] where \(s,k \in \mathbb R\), \(f\) is a locally Lipschitz function. They give theoretical and numerical evidence of solutions blowing up in finite time with infinitely many wild oscillations. An explicit example is presented where this phenomenon occurs. The authors also discuss possible applications to biharmonic partial differential equations and to the suspension bridge model, and give a possible new explanation of the collapse of bridges.
reviewed by: Cemil Tunç
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 5959720
zbMATH Keywords: blow up
zbMATH Keywords: oscillating solutions
zbMATH Keywords: fourth order differential equations
MaRDI profile type: Publication
full work available at URL: j.na.2011.06.049
OpenAlex ID: W2067536144
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DOI: 10.1016/J.NA.2011.06.049
description: scientific article; zbMATH DE number 5959720