Necessary and sufficient conditions for positive solutions of second-order nonlinear dynamic equations on time scales
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for positive solutions of second-order nonlinear dynamic equations on time scales
zbMATH Open document ID: 1217.34146
DOI: 10.1155/2011/769893
author: Zhi-Qiang Zhu
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2011-07-22T00:00:00Z
review text: Summary: This paper is concerned with the existence of nonoscillatory solutions for the nonlinear dynamic equation \((p(t)(\psi \circ x)(x^{\sigma})^{\Delta})^{\Delta} + q(t)f \circ x^{\sigma} = 0\) on time scales. By making use of the generalized Riccati transformation technique, we establish some necessary and sufficient criteria to guarantee the existence. The last examples show that our results can be applied on the differential equations, the difference equations, and the \(q\)-difference equations.
Mathematics Subject Classification ID: 34N05
zbMATH DE Number: 5930224
Wikidata QID: Q58687939
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/769893
OpenAlex ID: W2037687629
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description: scientific article; zbMATH DE number 5930224