Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations
The existence of multiple periodic solutions of the following differential delay equation 𝑥(𝑡)=−𝑓(𝑥(𝑡−𝑟)) is established by applying variational approaches directly, where 𝑥∈ℝ, 𝑓∈𝐶(ℝ,ℝ) and 𝑟>0 is a given constant. This means that we do not need to use Kaplan and Yorke's reduction technique...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/978137 |
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| author | Rong Cheng Jianhua Hu |
| author_facet | Rong Cheng Jianhua Hu |
| author_sort | Rong Cheng |
| collection | DOAJ |
| description | The existence of multiple periodic solutions of the following differential delay equation 𝑥(𝑡)=−𝑓(𝑥(𝑡−𝑟)) is established by applying variational approaches directly, where 𝑥∈ℝ, 𝑓∈𝐶(ℝ,ℝ) and 𝑟>0 is a given constant. This means that we do not need to use Kaplan and Yorke's reduction technique to reduce the existence problem of the above equation to an existence problem for a related coupled system. Such a reduction method introduced first by Kaplan and Yorke in (1974) is often employed in previous papers to study the existence of periodic solutions for the above equation and its similar ones by variational approaches. |
| format | Article |
| id | doaj-art-13e87bb1ca9b448592c9318b00636baf |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-13e87bb1ca9b448592c9318b00636baf2025-02-03T06:07:30ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/978137978137Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay EquationsRong Cheng0Jianhua Hu1College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaThe existence of multiple periodic solutions of the following differential delay equation 𝑥(𝑡)=−𝑓(𝑥(𝑡−𝑟)) is established by applying variational approaches directly, where 𝑥∈ℝ, 𝑓∈𝐶(ℝ,ℝ) and 𝑟>0 is a given constant. This means that we do not need to use Kaplan and Yorke's reduction technique to reduce the existence problem of the above equation to an existence problem for a related coupled system. Such a reduction method introduced first by Kaplan and Yorke in (1974) is often employed in previous papers to study the existence of periodic solutions for the above equation and its similar ones by variational approaches.http://dx.doi.org/10.1155/2010/978137 |
| spellingShingle | Rong Cheng Jianhua Hu Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations Abstract and Applied Analysis |
| title | Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations |
| title_full | Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations |
| title_fullStr | Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations |
| title_full_unstemmed | Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations |
| title_short | Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations |
| title_sort | variational approaches for the existence of multiple periodic solutions of differential delay equations |
| url | http://dx.doi.org/10.1155/2010/978137 |
| work_keys_str_mv | AT rongcheng variationalapproachesfortheexistenceofmultipleperiodicsolutionsofdifferentialdelayequations AT jianhuahu variationalapproachesfortheexistenceofmultipleperiodicsolutionsofdifferentialdelayequations |