Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach Spaces
By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem (-1)n-kun(t)=f(t,ut), 0<t<1, n≥2, 1≤k≤n-1, u(0)=∑i=1m-2aiu(ξi), u(i)(0)=u(j)(1)=θ, 1≤i≤k−1, 0≤j≤n−k−1 in a real Banach...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/727468 |
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| author | Yulin Zhao |
| author_facet | Yulin Zhao |
| author_sort | Yulin Zhao |
| collection | DOAJ |
| description | By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem (-1)n-kun(t)=f(t,ut), 0<t<1, n≥2, 1≤k≤n-1, u(0)=∑i=1m-2aiu(ξi), u(i)(0)=u(j)(1)=θ, 1≤i≤k−1, 0≤j≤n−k−1 in a real Banach space E, where θ is the zero element of E, 0 < ξ1 < ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2. As an application, we give two examples to demonstrate our results. |
| format | Article |
| id | doaj-art-eaa97f3ffd694e2887a9579cec9c9e8f |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-eaa97f3ffd694e2887a9579cec9c9e8f2025-08-20T02:22:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/727468727468Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach SpacesYulin Zhao0School of Science, Hunan University of Technology, Zhuzhou 412007, ChinaBy means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem (-1)n-kun(t)=f(t,ut), 0<t<1, n≥2, 1≤k≤n-1, u(0)=∑i=1m-2aiu(ξi), u(i)(0)=u(j)(1)=θ, 1≤i≤k−1, 0≤j≤n−k−1 in a real Banach space E, where θ is the zero element of E, 0 < ξ1 < ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2. As an application, we give two examples to demonstrate our results.http://dx.doi.org/10.1155/2012/727468 |
| spellingShingle | Yulin Zhao Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach Spaces |
| title_full | Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach Spaces |
| title_fullStr | Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach Spaces |
| title_full_unstemmed | Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach Spaces |
| title_short | Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach Spaces |
| title_sort | positive solutions for k n k conjugate multipoint boundary value problems in banach spaces |
| url | http://dx.doi.org/10.1155/2012/727468 |
| work_keys_str_mv | AT yulinzhao positivesolutionsforknkconjugatemultipointboundaryvalueproblemsinbanachspaces |