Oscillation criteria for certain nonlinear fourth order equations
type: Item
instance of: scholarly article
title: Oscillation criteria for certain nonlinear fourth order equations
zbMATH Open document ID: 0539.34021
DOI: 10.1155/S0161171283000502
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/45375
review text: The author considers the following equation: (1) \(y^{(4)}+p(t)y'+q(t)f(y)=0\), where (i) p',q,r are continuous functions on \([0,\infty)\) and \(p(t)>0\), \(q(t)>0\) on \([0,\infty)\), f is continuous on R and \(f(y)/y\geq m>0\) for \(y\neq 0\); (ii) \(mq-p'\geq 0\) on \([o,\infty)\). (2) \(y^{(4)}+p(t)y'+q(t)f(y)=r(t),\) where (i) and \(p'(t)<0\) on \([0,\infty)\), \(\int^{\infty}(r^ 2(t)/p'(t))dt>-\infty\) hold. Under these and other assumptions he establishes several criteria for the existence of oscillatory solutions of (1) and (2).
reviewed by: Pavol Marušiak
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 3857514
zbMATH Keywords: nonlinear fourth order equations
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: criteria
zbMATH Keywords: oscillatory solutions
author: Willie E. jun. Taylor
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3857514