Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations

Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations

We study perturbations of the nonoscillatory half-linear differential equation (r(t)Φ(x'))'+c(t)Φ(x)=0, Φ(x):=|x|p-2x, p>1. We find explicit formulas for the functions r̂, ĉ such that the equation [(r(t)+λr̂(t))Φ(x')]'+[c(t)+μĉ(t)]Φ(x)=0 is conditionally oscillatory, that is...

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Main Authors: Ondřej Došlý, Simona Fišnarová
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/182827
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spelling doaj-e4b743b667cc4860be43883508635da92020-11-24T22:06:44ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/182827182827Two-Parametric Conditionally Oscillatory Half-Linear Differential EquationsOndřej Došlý0Simona Fišnarová1Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech RepublicDepartment of Mathematics, Mendel University in Brno, Zemĕdĕlská 1, 613 00 Brno, Czech RepublicWe study perturbations of the nonoscillatory half-linear differential equation (r(t)Φ(x'))'+c(t)Φ(x)=0, Φ(x):=|x|p-2x, p>1. We find explicit formulas for the functions r̂, ĉ such that the equation [(r(t)+λr̂(t))Φ(x')]'+[c(t)+μĉ(t)]Φ(x)=0 is conditionally oscillatory, that is, there exists a constant γ such that the previous equation is oscillatory if μ-λ>γ and nonoscillatory if μ-λ<γ. The obtained results extend the previous results concerning two-parametric perturbations of the half-linear Euler differential equation.http://dx.doi.org/10.1155/2011/182827
collection DOAJ
language English
format Article
sources DOAJ
author Ondřej Došlý
Simona Fišnarová
spellingShingle Ondřej Došlý
Simona Fišnarová
Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations
Abstract and Applied Analysis
author_facet Ondřej Došlý
Simona Fišnarová
author_sort Ondřej Došlý
title Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations
title_short Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations
title_full Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations
title_fullStr Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations
title_full_unstemmed Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations
title_sort two-parametric conditionally oscillatory half-linear differential equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2011-01-01
description We study perturbations of the nonoscillatory half-linear differential equation (r(t)Φ(x'))'+c(t)Φ(x)=0, Φ(x):=|x|p-2x, p>1. We find explicit formulas for the functions r̂, ĉ such that the equation [(r(t)+λr̂(t))Φ(x')]'+[c(t)+μĉ(t)]Φ(x)=0 is conditionally oscillatory, that is, there exists a constant γ such that the previous equation is oscillatory if μ-λ>γ and nonoscillatory if μ-λ<γ. The obtained results extend the previous results concerning two-parametric perturbations of the half-linear Euler differential equation.
url http://dx.doi.org/10.1155/2011/182827
work_keys_str_mv AT ondrejdosly twoparametricconditionallyoscillatoryhalflineardifferentialequations
AT simonafisnarova twoparametricconditionallyoscillatoryhalflineardifferentialequations
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