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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Main Author: Yulin Zhao
Format: Article
Language:English
Published: Wiley 2012-01-01
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.
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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