Oscillation of Two-Dimensional Neutral Delay Dynamic Systems
We consider a class of nonlinear two-dimensional dynamic systems of the neutral type (x(t)-a(t)x(τ1(t)))Δ=p(t)f1(y(t)), yΔ(t)=-q(t)f2(x(τ2(t))). We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results when a(t)=0 improve the oscillation results for...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/871961 |
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| author | Xinli Zhang Shanliang Zhu |
| author_facet | Xinli Zhang Shanliang Zhu |
| author_sort | Xinli Zhang |
| collection | DOAJ |
| description | We consider a class of nonlinear two-dimensional dynamic systems of the neutral type (x(t)-a(t)x(τ1(t)))Δ=p(t)f1(y(t)), yΔ(t)=-q(t)f2(x(τ2(t))). We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results when a(t)=0 improve the oscillation results for dynamic systems on time scales that have been established by Fu and Lin (2010), since our results do not restrict to the case where f(u)=u. Also, as a special case when 𝕋=ℝ, our results do not require an to be a positive real sequence. Some examples are given to illustrate the main results. |
| format | Article |
| id | doaj-art-0667f4c05fd34823af7728ce778a0e95 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0667f4c05fd34823af7728ce778a0e952025-02-03T05:47:52ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/871961871961Oscillation of Two-Dimensional Neutral Delay Dynamic SystemsXinli Zhang0Shanliang Zhu1College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, ChinaCollege of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, ChinaWe consider a class of nonlinear two-dimensional dynamic systems of the neutral type (x(t)-a(t)x(τ1(t)))Δ=p(t)f1(y(t)), yΔ(t)=-q(t)f2(x(τ2(t))). We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results when a(t)=0 improve the oscillation results for dynamic systems on time scales that have been established by Fu and Lin (2010), since our results do not restrict to the case where f(u)=u. Also, as a special case when 𝕋=ℝ, our results do not require an to be a positive real sequence. Some examples are given to illustrate the main results.http://dx.doi.org/10.1155/2013/871961 |
| spellingShingle | Xinli Zhang Shanliang Zhu Oscillation of Two-Dimensional Neutral Delay Dynamic Systems Advances in Mathematical Physics |
| title | Oscillation of Two-Dimensional Neutral Delay Dynamic Systems |
| title_full | Oscillation of Two-Dimensional Neutral Delay Dynamic Systems |
| title_fullStr | Oscillation of Two-Dimensional Neutral Delay Dynamic Systems |
| title_full_unstemmed | Oscillation of Two-Dimensional Neutral Delay Dynamic Systems |
| title_short | Oscillation of Two-Dimensional Neutral Delay Dynamic Systems |
| title_sort | oscillation of two dimensional neutral delay dynamic systems |
| url | http://dx.doi.org/10.1155/2013/871961 |
| work_keys_str_mv | AT xinlizhang oscillationoftwodimensionalneutraldelaydynamicsystems AT shanliangzhu oscillationoftwodimensionalneutraldelaydynamicsystems |