Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments
The behaviour of solutions for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique sol...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/213935 |
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| _version_ | 1832556482358411264 |
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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 for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results not only are new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the results are justified with examples. |
| format | Article |
| id | doaj-art-8e6395db4afa4c019539a80ac6ce1ec5 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-8e6395db4afa4c019539a80ac6ce1ec52025-02-03T05:45:15ZengWileyInternational Journal of Differential Equations1687-96431687-96512015-01-01201510.1155/2015/213935213935Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating ArgumentsA. 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 for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results not only are new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the results are justified with examples.http://dx.doi.org/10.1155/2015/213935 |
| spellingShingle | A. T. Ademola B. S. Ogundare M. O. Ogundiran O. A. Adesina Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments International Journal of Differential Equations |
| title | Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments |
| title_full | Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments |
| title_fullStr | Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments |
| title_full_unstemmed | Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments |
| title_short | Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments |
| title_sort | stability boundedness and existence of periodic solutions to certain third order delay differential equations with multiple deviating arguments |
| url | http://dx.doi.org/10.1155/2015/213935 |
| work_keys_str_mv | AT atademola stabilityboundednessandexistenceofperiodicsolutionstocertainthirdorderdelaydifferentialequationswithmultipledeviatingarguments AT bsogundare stabilityboundednessandexistenceofperiodicsolutionstocertainthirdorderdelaydifferentialequationswithmultipledeviatingarguments AT moogundiran stabilityboundednessandexistenceofperiodicsolutionstocertainthirdorderdelaydifferentialequationswithmultipledeviatingarguments AT oaadesina stabilityboundednessandexistenceofperiodicsolutionstocertainthirdorderdelaydifferentialequationswithmultipledeviatingarguments |