Two-parametric conditionally oscillatory half-linear differential equations
type: Item
instance of: scholarly article
title: Two-parametric conditionally oscillatory half-linear differential equations
zbMATH Open document ID: 1217.34054
DOI: 10.1155/2011/182827
author: Ondřej Došlý
author: Simona Fisnarova
published in: Abstract and Applied Analysis
publication date: 2011-05-16T00:00:00Z
review text: Summary: We study perturbations of the nonoscillatory half-linear differential equation \[ (r(t)\Phi(x'))'+c(t)\Phi(x)=0, \] \(\Phi(x):=|x|^{p-2}x,\) \(p>1\). We find explicit formulas for the functions \(\widehat r\), \(\widehat c\) such that the equation \[ [(r(t)+\lambda\widehat r(t)) \Phi(x')]'+[c(t)+\mu\widehat c(t)] \Phi (x)=0 \] is conditionally oscillatory, that is, there exists a constant \(\gamma\) such that the previous equation is oscillatory if \(\mu-\lambda>\gamma\) and nonoscillatory if \(\mu-\lambda <\gamma\). The obtained results extend previous results concerning two-parametric perturbations of the half-linear Euler differential equation.
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 5888121
zbMATH Keywords: nonoscillatory half-linear differential equation
zbMATH Keywords: two-parametric perturbations
zbMATH Keywords: Euler differential equation
Wikidata QID: Q58654052
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/182827
OpenAlex ID: W2063361500
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description: scientific article; zbMATH DE number 5888121