Forced oscillation of second-order half-linear dynamic equations on time scales
type: Item
instance of: scholarly article
title: Forced oscillation of second-order half-linear dynamic equations on time scales
zbMATH Open document ID: 1205.34134
DOI: 10.1155/2010/294194
author: Quanwen Lin
author: Baoguo Jia
author: Qiru Wang
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/224726
review text: Summary: We establish a new interval oscillation criterion for the second-order half-linear dynamic equation \[ (r(t)[x^\Delta(t)]^\alpha)^\Delta+p(t)x^\alpha(\sigma(t))=f(t) \] on a time scale \(\mathbb T\) which is unbounded. This criterion is an extension of the oscillation result for second order linear dynamic equation established by \textit{L. Erbe, A. Peterson} and \textit{S. H. Saker} [J. Difference Equ. Appl. 14, No.~10--11, 997--1009 (2008; Zbl 1168.34025)]. As an application, we obtain a sufficient condition for oscillation of the second-order half-linear differential equation \[ ([x'(t)]^\alpha)'+c\sin tx^\alpha(t)=\cos t, \] where \(\alpha=p/q\), \(p, q\) are odd positive integers.
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34K11
zbMATH DE Number: 5791615
Wikidata QID: Q58649817
MaRDI profile type: Publication
OpenAlex ID: W2075373707
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description: scientific article; zbMATH DE number 5791615