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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/546302 |
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| _version_ | 1832562718543970304 |
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| author | Zeqing Liu Yuguang Xu Shin Min Kang Young Chel Kwun |
| author_facet | Zeqing Liu Yuguang Xu Shin Min Kang Young Chel Kwun |
| author_sort | Zeqing Liu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-13c425ccb9ff4a31a85daf88d6f7bc53 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-13c425ccb9ff4a31a85daf88d6f7bc532025-02-03T01:21:55ZengWileyAbstract 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 |
| spellingShingle | Zeqing Liu Yuguang Xu Shin Min Kang Young Chel Kwun Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation Abstract and Applied Analysis |
| title | 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_short | Bounded Oscillation of a Forced Nonlinear Neutral Differential Equation |
| title_sort | bounded oscillation of a forced nonlinear neutral differential equation |
| 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 |