On some properties of positive solutions for a third-order three-point boundary value problem with a parameter
Abstract In this article, we discuss some properties of positive solutions for a third-order differential equation with three-point boundary conditions and a positive parameter. By using recent fixed point theory, we establish the existence and uniqueness of positive solutions for any given paramete...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-06-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-017-1246-7 |
| _version_ | 1818623657740599296 |
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| author | Chengbo Zhai Li Zhao Shunyong Li HR Marasi |
| author_facet | Chengbo Zhai Li Zhao Shunyong Li HR Marasi |
| author_sort | Chengbo Zhai |
| collection | DOAJ |
| description | Abstract In this article, we discuss some properties of positive solutions for a third-order differential equation with three-point boundary conditions and a positive parameter. By using recent fixed point theory, we establish the existence and uniqueness of positive solutions for any given parameter, and we show that the positive solution is continuous, increasing with respect to the parameter. Moreover, we give some properties of limits for positive solutions. An example is provided to demonstrate the main result. |
| first_indexed | 2024-12-16T18:44:33Z |
| format | Article |
| id | doaj.art-a00b8dce1a5d4cb08a916343996480b6 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T18:44:33Z |
| publishDate | 2017-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-a00b8dce1a5d4cb08a916343996480b62022-12-21T22:20:54ZengSpringerOpenAdvances in Difference Equations1687-18472017-06-012017111110.1186/s13662-017-1246-7On some properties of positive solutions for a third-order three-point boundary value problem with a parameterChengbo Zhai0Li Zhao1Shunyong Li2HR Marasi3School of Mathematical Sciences, Shanxi UniversitySchool of Mathematical Sciences, Shanxi UniversitySchool of Mathematical Sciences, Shanxi UniversityUniversity of TabrizAbstract In this article, we discuss some properties of positive solutions for a third-order differential equation with three-point boundary conditions and a positive parameter. By using recent fixed point theory, we establish the existence and uniqueness of positive solutions for any given parameter, and we show that the positive solution is continuous, increasing with respect to the parameter. Moreover, we give some properties of limits for positive solutions. An example is provided to demonstrate the main result.http://link.springer.com/article/10.1186/s13662-017-1246-7third-order differential equationthree-point boundary value problemfixed point theoryproperties of positive solutions |
| spellingShingle | Chengbo Zhai Li Zhao Shunyong Li HR Marasi On some properties of positive solutions for a third-order three-point boundary value problem with a parameter Advances in Difference Equations third-order differential equation three-point boundary value problem fixed point theory properties of positive solutions |
| title | On some properties of positive solutions for a third-order three-point boundary value problem with a parameter |
| title_full | On some properties of positive solutions for a third-order three-point boundary value problem with a parameter |
| title_fullStr | On some properties of positive solutions for a third-order three-point boundary value problem with a parameter |
| title_full_unstemmed | On some properties of positive solutions for a third-order three-point boundary value problem with a parameter |
| title_short | On some properties of positive solutions for a third-order three-point boundary value problem with a parameter |
| title_sort | on some properties of positive solutions for a third order three point boundary value problem with a parameter |
| topic | third-order differential equation three-point boundary value problem fixed point theory properties of positive solutions |
| url | http://link.springer.com/article/10.1186/s13662-017-1246-7 |
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