Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations
The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions t...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2016/2843709 |
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| _version_ | 1832545523820658688 |
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| author | A. T. Ademola B. S. Ogundare M. O. Ogundiran O. A. Adesina |
| author_facet | A. T. Ademola B. S. Ogundare M. O. Ogundiran O. A. Adesina |
| author_sort | A. T. Ademola |
| collection | DOAJ |
| description | The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results are new and also complement related ones that have appeared in the literature. Moreover, examples are given to illustrate the feasibility and correctness of the main results. |
| format | Article |
| id | doaj-art-9882258681c8477498373744acdd881f |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-9882258681c8477498373744acdd881f2025-02-03T07:25:32ZengWileyInternational Journal of Differential Equations1687-96431687-96512016-01-01201610.1155/2016/28437092843709Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential EquationsA. T. Ademola0B. S. Ogundare1M. O. Ogundiran2O. A. Adesina3Research Group in Differential Equations and Applications (RGDEA), Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, NigeriaResearch Group in Differential Equations and Applications (RGDEA), Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, NigeriaResearch Group in Differential Equations and Applications (RGDEA), Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, NigeriaResearch Group in Differential Equations and Applications (RGDEA), Department of Mathematics, Obafemi Awolowo University, Ile-Ife 220005, NigeriaThe behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results are new and also complement related ones that have appeared in the literature. Moreover, examples are given to illustrate the feasibility and correctness of the main results.http://dx.doi.org/10.1155/2016/2843709 |
| spellingShingle | A. T. Ademola B. S. Ogundare M. O. Ogundiran O. A. Adesina Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations International Journal of Differential Equations |
| title | Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations |
| title_full | Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations |
| title_fullStr | Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations |
| title_full_unstemmed | Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations |
| title_short | Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations |
| title_sort | periodicity stability and boundedness of solutions to certain second order delay differential equations |
| url | http://dx.doi.org/10.1155/2016/2843709 |
| work_keys_str_mv | AT atademola periodicitystabilityandboundednessofsolutionstocertainsecondorderdelaydifferentialequations AT bsogundare periodicitystabilityandboundednessofsolutionstocertainsecondorderdelaydifferentialequations AT moogundiran periodicitystabilityandboundednessofsolutionstocertainsecondorderdelaydifferentialequations AT oaadesina periodicitystabilityandboundednessofsolutionstocertainsecondorderdelaydifferentialequations |