The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations
The present paper proposes a new monotone iteration principle for the existence as well as approximations of the coupled solutions for a coupled periodic boundary value problem of second order ordinary nonlinear differential equations. An algorithm for the coupled solutions is developed and it is sh...
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| Format: | Article |
| Language: | English |
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Etamaths Publishing
2015-05-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://www.etamaths.com/index.php/ijaa/article/view/518 |
| _version_ | 1818675224846008320 |
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| author | Bapurao C. Dhage |
| author_facet | Bapurao C. Dhage |
| author_sort | Bapurao C. Dhage |
| collection | DOAJ |
| description | The present paper proposes a new monotone iteration principle for the existence as well as approximations of the coupled solutions for a coupled periodic boundary value problem of second order ordinary nonlinear differential equations. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper. We claim that the method as well as the results of this paper are new to literature on nonlinear analysis and applications. |
| first_indexed | 2024-12-17T08:24:11Z |
| format | Article |
| id | doaj.art-f2a0b44e9b604fe98aa8bad211aeadc6 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-17T08:24:11Z |
| publishDate | 2015-05-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-f2a0b44e9b604fe98aa8bad211aeadc62022-12-21T21:56:51ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392015-05-01815362127The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential EquationsBapurao C. Dhage0kasubai, Gurukul Colony, AhmedpurThe present paper proposes a new monotone iteration principle for the existence as well as approximations of the coupled solutions for a coupled periodic boundary value problem of second order ordinary nonlinear differential equations. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper. We claim that the method as well as the results of this paper are new to literature on nonlinear analysis and applications.http://www.etamaths.com/index.php/ijaa/article/view/518 |
| spellingShingle | Bapurao C. Dhage The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations International Journal of Analysis and Applications |
| title | The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations |
| title_full | The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations |
| title_fullStr | The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations |
| title_full_unstemmed | The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations |
| title_short | The Dhage Iteration Principle for Coupled PBVPs of Nonlinear Second Order Differential Equations |
| title_sort | dhage iteration principle for coupled pbvps of nonlinear second order differential equations |
| url | http://www.etamaths.com/index.php/ijaa/article/view/518 |
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