Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values

The paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations...

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Main Authors:	Hasil Petr, Veselý Michal
Format:	Article
Language:	English
Published:	De Gruyter 2018-05-01
Series:	Open Mathematics
Subjects:	half-linear equation oscillation theory riccati technique oscillation constant conditional oscillation 34c10 34c15
Online Access:	https://doi.org/10.1515/math-2018-0047

id	doaj-c622b1cde63b4bf1b0fd445db5c4081e
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spelling	doaj-c622b1cde63b4bf1b0fd445db5c4081e2021-09-06T19:20:10ZengDe GruyterOpen Mathematics2391-54552018-05-0116150752110.1515/math-2018-0047math-2018-0047Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean valuesHasil Petr0Veselý Michal1Department of Mathematics, Faculty of Forestry and Wood Technology, Mendel University in Brno, Zemědělská 1, CZ-613 00Brno, Czech RepublicDepartment of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-611 37Brno, Czech RepublicThe paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.https://doi.org/10.1515/math-2018-0047half-linear equationoscillation theoryriccati techniqueoscillation constantconditional oscillation34c1034c15
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Hasil Petr Veselý Michal
spellingShingle	Hasil Petr Veselý Michal Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values Open Mathematics half-linear equation oscillation theory riccati technique oscillation constant conditional oscillation 34c10 34c15
author_facet	Hasil Petr Veselý Michal
author_sort	Hasil Petr
title	Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values
title_short	Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values
title_full	Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values
title_fullStr	Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values
title_full_unstemmed	Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values
title_sort	oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values
publisher	De Gruyter
series	Open Mathematics
issn	2391-5455
publishDate	2018-05-01
description	The paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.
topic	half-linear equation oscillation theory riccati technique oscillation constant conditional oscillation 34c10 34c15
url	https://doi.org/10.1515/math-2018-0047
work_keys_str_mv	AT hasilpetr oscillationandnonoscillationofhalflineardifferentialequationswithcoeffcientsdeterminedbyfunctionshavingmeanvalues AT veselymichal oscillationandnonoscillationofhalflineardifferentialequationswithcoeffcientsdeterminedbyfunctionshavingmeanvalues
_version_	1717777180465823744

Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values

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