Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions

Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions

The continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for a 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 for function g. It is proved that all solutions can be ex...

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Main Authors: Lianwen Wang, Rhonda McKee
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/313725
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spelling doaj-abbc5e311f144bdb918a7a2d2dca63822020-11-25T00:18:28ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/313725313725Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity AssumptionsLianwen Wang0Rhonda McKee1Department of Mathematics and Computer Science, University of Central Missouri, Warrensburg, MO 64093, USADepartment of Mathematics and Computer Science, University of Central Missouri, Warrensburg, MO 64093, USAThe continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for a 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 for 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.http://dx.doi.org/10.1155/2012/313725
collection DOAJ
language English
format Article
sources DOAJ
author Lianwen Wang
Rhonda McKee
spellingShingle Lianwen Wang
Rhonda McKee
Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions
Journal of Applied Mathematics
author_facet Lianwen Wang
Rhonda McKee
author_sort Lianwen Wang
title Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions
title_short Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions
title_full Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions
title_fullStr Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions
title_full_unstemmed Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions
title_sort nonoscillatory solutions of second-order differential equations without monotonicity assumptions
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description The continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for a 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 for 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.
url http://dx.doi.org/10.1155/2012/313725
work_keys_str_mv AT lianwenwang nonoscillatorysolutionsofsecondorderdifferentialequationswithoutmonotonicityassumptions
AT rhondamckee nonoscillatorysolutionsofsecondorderdifferentialequationswithoutmonotonicityassumptions
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