Nonoscillation theory for second order half-linear differential equations in the framework of regular variation
type: Item
instance of: scholarly article
title: Nonoscillation theory for second order half-linear differential equations in the framework of regular variation
zbMATH Open document ID: 1047.34034
DOI: 10.1007/BF03322729
author: Jaroslav Jaroš
author: Kusano Takaŝi
author: T. Tanigawa
published in: Results in Mathematics
publication date: 2003-11-10T00:00:00Z
review text: The authors study regularity properties implying nonoscillation of the solutions of the half-linear equation \[ (| y'|^{\alpha- 1}y')'+ q(t)| y|^{\alpha- 1}y= 0 \] with \(\alpha> 0\) and \(q\) positive and continuous on the half-axis \(t\geq 0\). Some necessary and sufficient conditions for the existence of such solutions are presented. The results generalize corresponding ones for the linear equation (when \(\alpha= 1\)) as proved in [\textit{V. Marić}, Regular variation and differential equations. Lecture Notes in Mathematics 1726. Berlin: Springer-Verlag (2000; Zbl 0946.34001)].
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 26A12
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 2002348
zbMATH Keywords: half-linear equation
zbMATH Keywords: regularly varying solutions
zbMATH Keywords: nonoscillation
reviewed by: Vojislav Marić
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322729
OpenAlex ID: W2023042074
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description: scientific article; zbMATH DE number 2002348