Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations
We are concerned with oscillation of the first order neutral delay differential equation [x(t)−px(t−τ)]′+qx(t−σ)=0 with constant coefficients, and we obtain some necessary and sufficient conditions of oscillation for all the solutions in respective cases 0<p<1 and p>1.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/623713 |
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doaj-b23b7d0a44d74cb09d8b0f2437e6027d2020-11-24T23:11:58ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/623713623713Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential EquationsSongbai Guo0Youjian Shen1Binbin Shi2School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Statistics, Hainan Normal University, Haikou 571158, ChinaDepartment of Mathematics and Information Science, Shandong Agricultural University, Tai’an 271018, ChinaWe are concerned with oscillation of the first order neutral delay differential equation [x(t)−px(t−τ)]′+qx(t−σ)=0 with constant coefficients, and we obtain some necessary and sufficient conditions of oscillation for all the solutions in respective cases 0<p<1 and p>1.http://dx.doi.org/10.1155/2014/623713 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Songbai Guo Youjian Shen Binbin Shi |
| spellingShingle |
Songbai Guo Youjian Shen Binbin Shi Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations Abstract and Applied Analysis |
| author_facet |
Songbai Guo Youjian Shen Binbin Shi |
| author_sort |
Songbai Guo |
| title |
Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations |
| title_short |
Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations |
| title_full |
Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations |
| title_fullStr |
Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations |
| title_full_unstemmed |
Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations |
| title_sort |
necessary and sufficient conditions of oscillation in first order neutral delay differential equations |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| description |
We are concerned with oscillation of the first order neutral delay differential equation [x(t)−px(t−τ)]′+qx(t−σ)=0 with constant coefficients, and we obtain some necessary and sufficient conditions of oscillation for all the solutions in respective cases 0<p<1 and p>1. |
| url |
http://dx.doi.org/10.1155/2014/623713 |
| work_keys_str_mv |
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| _version_ |
1725603183580938240 |