Oscillation theorems for differential equations with a nonlinear damping term
type: Item
instance of: scholarly article
title: Oscillation theorems for differential equations with a nonlinear damping term
zbMATH Open document ID: 1027.34040
DOI: 10.1016/S0022-247X(02)00623-6
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: The authors investigate oscillatory properties of the nonlinear second-order differential equation \[ (r(t)k_1(x,x'))' +p(t)k_2(x,x')x'+q(t)f(x)=0,\tag{*} \] under natural restrictions on the functions \(r,k_1,k_2,p,q\) and \(f\). Using a modified \(H\)-function averaging technique introduced for linear equations by \textit{Ch. G. Philos} [Arch. Math. 53, 482-492 (1989; Zbl 0661.34030)], additional conditions are found which guarantee that (*) possesses no nonoscillatory solution. The results of the paper are illustrated by a number of examples showing that the obtained criteria apply in situations where known criteria fail.
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1915737
zbMATH Keywords: nonlinear differential equations
zbMATH Keywords: nonlinear damping term
zbMATH Keywords: proper solutions
zbMATH Keywords: integral averaging method
author: Svitlana P. Rogovchenko
author: Yuriy V. Rogovchenko
reviewed by: Ondřej Došlý
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915737