Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems

Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems

We study the existence and multiplicity of positive solutions for a class of nth-order singular nonlocal boundary value problemsu(n)(t)+a(t)f(t,u)=0, t∈(0,1), u(0)=0, u'(0)=0, …,u(n−2)(0)=0, αu(η)=u(1), where 0<η<1,  0<αηn−1 <...

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Main Authors: Xin&#39;an Hao, Lishan Liu, Yonghong Wu
Format: Article
Language:English
Published: SpringerOpen 2007-04-01
Series:Boundary Value Problems
Online Access:http://dx.doi.org/10.1155/2007/74517
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spelling doaj-13cd1d83e137434fb40c6b9d34d99bcb2020-11-24T21:07:56ZengSpringerOpenBoundary Value Problems1687-27621687-27702007-04-01200710.1155/2007/74517Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value ProblemsXin&#39;an HaoLishan LiuYonghong WuWe study the existence and multiplicity of positive solutions for a class of nth-order singular nonlocal boundary value problemsu(n)(t)+a(t)f(t,u)=0, t∈(0,1), u(0)=0, u'(0)=0, …,u(n−2)(0)=0, αu(η)=u(1), where 0<η<1,  0<αηn−1 <1. The singularity may appear at t=0 and/or t=1. The Krasnosel'skii-Guo theorem on cone expansion and compression is used in this study. The main results improve and generalize the existing results.http://dx.doi.org/10.1155/2007/74517
collection DOAJ
language English
format Article
sources DOAJ
author Xin&#39;an Hao
Lishan Liu
Yonghong Wu
spellingShingle Xin&#39;an Hao
Lishan Liu
Yonghong Wu
Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems
Boundary Value Problems
author_facet Xin&#39;an Hao
Lishan Liu
Yonghong Wu
author_sort Xin&#39;an Hao
title Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems
title_short Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems
title_full Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems
title_fullStr Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems
title_full_unstemmed Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems
title_sort positive solutions for nonlinear nth-order singular nonlocal boundary value problems
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2762
1687-2770
publishDate 2007-04-01
description We study the existence and multiplicity of positive solutions for a class of nth-order singular nonlocal boundary value problemsu(n)(t)+a(t)f(t,u)=0, t∈(0,1), u(0)=0, u'(0)=0, …,u(n−2)(0)=0, αu(η)=u(1), where 0<η<1,  0<αηn−1 <1. The singularity may appear at t=0 and/or t=1. The Krasnosel'skii-Guo theorem on cone expansion and compression is used in this study. The main results improve and generalize the existing results.
url http://dx.doi.org/10.1155/2007/74517
work_keys_str_mv AT xin39anhao positivesolutionsfornonlinearnthordersingularnonlocalboundaryvalueproblems
AT lishanliu positivesolutionsfornonlinearnthordersingularnonlocalboundaryvalueproblems
AT yonghongwu positivesolutionsfornonlinearnthordersingularnonlocalboundaryvalueproblems
_version_ 1716761505671675904

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