Nonoscillatory solutions of second-order differential equations without monotonicity assumptions
type: Item
instance of: scholarly article
title: Nonoscillatory solutions of second-order differential equations without monotonicity assumptions
zbMATH Open document ID: 1255.34033
DOI: 10.1155/2012/313725
author: Lianwen Wang
author: Rhonda L. McKee
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: The continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for the class of second-order nonlinear differential equations \[ [p(t)h(x(t))f(x'(t))]' = q(t)g(x(t)) \] are discussed without monotonicity assumption on the function \(g\). It is proved that all solutions can be extended to infinity, are eventually monotonic and can be classified into disjoint classes that are fully characterized in terms of several integral conditions. Moreover, necessary and sufficient conditions for the existence of solutions in each class and for the boundedness of all solutions are established.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 6106174
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/313725
OpenAlex ID: W2097550237
Wikidata QID: Q58906631
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DBLP publication ID: journals/jam/WangM12a
description: scientific article; zbMATH DE number 6106174