Conditionally oscillatory half-linear differential equations
type: Item
instance of: scholarly article
title: Conditionally oscillatory half-linear differential equations
zbMATH Open document ID: 1199.34169
author: Ondřej Došlý
author: Mehmet Ünal
published in: Acta Mathematica Hungarica
publication date: 2008-10-21T00:00:00Z
review text: The authors assume that a nonoscillatory solution to the half-linear equation \[ (r(t)\Phi(x'))+c(t)\Phi(x)=0,\;\Phi(x)=| x| ^{p-2}x,\;p>1, \] is known. Then they are able to construct a function \(d\) such that the (perturbed) equation \[ (r(t)\Phi(x'))+(c(t)+\lambda d(t))\Phi(x)=0 \] is conditionally oscillatory. They also establish an asymptotic formula for a solution of the perturbed equation in the critical case, i.e., when \(\lambda\) equals the oscillation constant. These results are then used to obtain new (non)oscillation criteria, which extend previous results for perturbed half-linear Euler type and Euler-Weber type equations. The concepts of generalized Riccati equation and of principal solution, and the Schauder-Tychonoff fixed point theorem play an important role in the proofs.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5355153
zbMATH Keywords: half-linear oscillation theory
zbMATH Keywords: conditionally oscillatory equation
zbMATH Keywords: oscillation and nonoscillation criteria
zbMATH Keywords: Riccati type equation
reviewed by: Pavel Rehak
MaRDI profile type: Publication
full work available at URL: s10474-007-7120-4
OpenAlex ID: W2014167750
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DOI: 10.1007/S10474-007-7120-4
description: scientific article; zbMATH DE number 5355153