Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems
Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In t...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/519346 |
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| _version_ | 1849473133836238848 |
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| author | Liu Yang Chunfang Shen Dapeng Xie |
| author_facet | Liu Yang Chunfang Shen Dapeng Xie |
| author_sort | Liu Yang |
| collection | DOAJ |
| description | Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper. |
| format | Article |
| id | doaj-art-d8e6d45b7d464d1195b3da832be06938 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d8e6d45b7d464d1195b3da832be069382025-08-20T03:24:16ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/519346519346Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value ProblemsLiu Yang0Chunfang Shen1Dapeng Xie2Department of Mathematics, Hefei Normal University, Hefei, Anhui 230061, ChinaDepartment of Mathematics, Hefei Normal University, Hefei, Anhui 230061, ChinaDepartment of Mathematics, Hefei Normal University, Hefei, Anhui 230061, ChinaPositive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.http://dx.doi.org/10.1155/2013/519346 |
| spellingShingle | Liu Yang Chunfang Shen Dapeng Xie Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems Abstract and Applied Analysis |
| title | Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems |
| title_full | Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems |
| title_fullStr | Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems |
| title_full_unstemmed | Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems |
| title_short | Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems |
| title_sort | positive solutions for resonant and nonresonant nonlinear third order multipoint boundary value problems |
| url | http://dx.doi.org/10.1155/2013/519346 |
| work_keys_str_mv | AT liuyang positivesolutionsforresonantandnonresonantnonlinearthirdordermultipointboundaryvalueproblems AT chunfangshen positivesolutionsforresonantandnonresonantnonlinearthirdordermultipointboundaryvalueproblems AT dapengxie positivesolutionsforresonantandnonresonantnonlinearthirdordermultipointboundaryvalueproblems |