Some Existence Results of Positive Solution to Second-Order Boundary Value Problems
We study the existence of positive and monotone solution to the boundary value problem u′′(t)+f(t,u(t))=0, 0⩽t⩽1, u(0)=ξu(1), u'(1)=ηu'(0), where ξ,η∈(0,1)∪(1,∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O’Regan....
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/516452 |
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| author | Shuhong Li Xiaoping Zhang Yongping Sun |
| author_facet | Shuhong Li Xiaoping Zhang Yongping Sun |
| author_sort | Shuhong Li |
| collection | DOAJ |
| description | We study the existence of positive and monotone solution to the boundary value problem u′′(t)+f(t,u(t))=0, 0⩽t⩽1, u(0)=ξu(1), u'(1)=ηu'(0), where ξ,η∈(0,1)∪(1,∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O’Regan. Finally, four examples are provided to demonstrate the availability of our main results. |
| format | Article |
| id | doaj-art-c6f1a4a50d0f45e39ddff8d3247dd32f |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c6f1a4a50d0f45e39ddff8d3247dd32f2025-08-20T03:22:58ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/516452516452Some Existence Results of Positive Solution to Second-Order Boundary Value ProblemsShuhong Li0Xiaoping Zhang1Yongping Sun2School of Medicine and School of Science, Lishui University, Lishui, Zhejiang 323000, ChinaSchool of Electron and Information, Zhejiang University of Media and Communications, Hangzhou, Zhejiang 310018, ChinaSchool of Electron and Information, Zhejiang University of Media and Communications, Hangzhou, Zhejiang 310018, ChinaWe study the existence of positive and monotone solution to the boundary value problem u′′(t)+f(t,u(t))=0, 0⩽t⩽1, u(0)=ξu(1), u'(1)=ηu'(0), where ξ,η∈(0,1)∪(1,∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O’Regan. Finally, four examples are provided to demonstrate the availability of our main results.http://dx.doi.org/10.1155/2014/516452 |
| spellingShingle | Shuhong Li Xiaoping Zhang Yongping Sun Some Existence Results of Positive Solution to Second-Order Boundary Value Problems Abstract and Applied Analysis |
| title | Some Existence Results of Positive Solution to Second-Order Boundary Value Problems |
| title_full | Some Existence Results of Positive Solution to Second-Order Boundary Value Problems |
| title_fullStr | Some Existence Results of Positive Solution to Second-Order Boundary Value Problems |
| title_full_unstemmed | Some Existence Results of Positive Solution to Second-Order Boundary Value Problems |
| title_short | Some Existence Results of Positive Solution to Second-Order Boundary Value Problems |
| title_sort | some existence results of positive solution to second order boundary value problems |
| url | http://dx.doi.org/10.1155/2014/516452 |
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