Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two...
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| Format: | Article |
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Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/635926 |
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doaj-c062bc5b420e40dd9b139f788949810a2020-11-25T00:24:43ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/635926635926Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in ApplicationsRong Cheng0College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaWe study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two given constants. By using a symplectic transformation constructed by Cheng (2010) and a result in Hamiltonian systems, the existence of oscillatory periodic solutions of the above-mentioned equations is established.http://dx.doi.org/10.1155/2011/635926 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Rong Cheng |
| spellingShingle |
Rong Cheng Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications Abstract and Applied Analysis |
| author_facet |
Rong Cheng |
| author_sort |
Rong Cheng |
| title |
Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications |
| title_short |
Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications |
| title_full |
Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications |
| title_fullStr |
Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications |
| title_full_unstemmed |
Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications |
| title_sort |
oscillatory periodic solutions for two differential-difference equations arising in applications |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2011-01-01 |
| description |
We study the existence of oscillatory periodic solutions for two nonautonomous differential-difference equations which arise in a variety of applications with the following forms: ẋ(t)=-f(t,x(t-r)) and ẋ(t)=-f(t,x(t-s))-f(t,x(t-2s)), where f∈C(R×R,R) is odd with respect to x, and r,s>0 are two given constants. By using a symplectic transformation constructed by Cheng (2010) and a result in Hamiltonian systems, the existence of oscillatory periodic solutions of the above-mentioned equations is established. |
| url |
http://dx.doi.org/10.1155/2011/635926 |
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AT rongcheng oscillatoryperiodicsolutionsfortwodifferentialdifferenceequationsarisinginapplications |
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