Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation

Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation

This paper is concerned with the nth-order forced nonlinear neutral differential equation [x(t)-p(t)x(τ(t))](n)+∑i=1mqi(t)fi(x(σi1(t)),x(σi2(t)),…,x(σiki(t)))=g(t),  t≥t0. Some necessary and sufficient conditions for the oscillation of bounded solutions and several sufficient conditions for the exis...

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Main Authors: Zeqing Liu, Yuguang Xu, Shin Min Kang, Young Chel Kwun
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/546302
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spelling doaj-13c425ccb9ff4a31a85daf88d6f7bc532020-11-24T22:22:38ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/546302546302Bounded Oscillation of a Forced Nonlinear Neutral Differential EquationZeqing Liu0Yuguang Xu1Shin Min Kang2Young Chel Kwun3Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, ChinaDepartment of Mathematics, Kunming University, Kunming, Yunnan 650214, ChinaDepartment of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of KoreaDepartment of Mathematics, Dong-A University, Pusan 614-714, Republic of KoreaThis paper is concerned with the nth-order forced nonlinear neutral differential equation [x(t)-p(t)x(τ(t))](n)+∑i=1mqi(t)fi(x(σi1(t)),x(σi2(t)),…,x(σiki(t)))=g(t),  t≥t0. Some necessary and sufficient conditions for the oscillation of bounded solutions and several sufficient conditions for the existence of uncountably many bounded positive and negative solutions of the above equation are established. The results obtained in this paper improve and extend essentially some known results in the literature. Five interesting examples that point out the importance of our results are also included.http://dx.doi.org/10.1155/2012/546302
collection DOAJ
language English
format Article
sources DOAJ
author Zeqing Liu
Yuguang Xu
Shin Min Kang
Young Chel Kwun
spellingShingle Zeqing Liu
Yuguang Xu
Shin Min Kang
Young Chel Kwun
Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation
Abstract and Applied Analysis
author_facet Zeqing Liu
Yuguang Xu
Shin Min Kang
Young Chel Kwun
author_sort Zeqing Liu
title Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation
title_short Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation
title_full Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation
title_fullStr Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation
title_full_unstemmed Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation
title_sort bounded oscillation of a forced nonlinear neutral differential equation
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description This paper is concerned with the nth-order forced nonlinear neutral differential equation [x(t)-p(t)x(τ(t))](n)+∑i=1mqi(t)fi(x(σi1(t)),x(σi2(t)),…,x(σiki(t)))=g(t),  t≥t0. Some necessary and sufficient conditions for the oscillation of bounded solutions and several sufficient conditions for the existence of uncountably many bounded positive and negative solutions of the above equation are established. The results obtained in this paper improve and extend essentially some known results in the literature. Five interesting examples that point out the importance of our results are also included.
url http://dx.doi.org/10.1155/2012/546302
work_keys_str_mv AT zeqingliu boundedoscillationofaforcednonlinearneutraldifferentialequation
AT yuguangxu boundedoscillationofaforcednonlinearneutraldifferentialequation
AT shinminkang boundedoscillationofaforcednonlinearneutraldifferentialequation
AT youngchelkwun boundedoscillationofaforcednonlinearneutraldifferentialequation
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