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 <...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2007-04-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2007/74517 |
| _version_ | 1819073380531306496 |
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| author | Xin'an Hao Lishan Liu Yonghong Wu |
| author_facet | Xin'an Hao Lishan Liu Yonghong Wu |
| author_sort | Xin'an Hao |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-21T17:52:42Z |
| format | Article |
| id | doaj.art-13cd1d83e137434fb40c6b9d34d99bcb |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-12-21T17:52:42Z |
| publishDate | 2007-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-13cd1d83e137434fb40c6b9d34d99bcb2022-12-21T18:55:18ZengSpringerOpenBoundary Value Problems1687-27621687-27702007-04-01200710.1155/2007/74517Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value ProblemsXin'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 |
| spellingShingle | Xin'an Hao Lishan Liu Yonghong Wu Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems Boundary Value Problems |
| title | 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_short | Positive Solutions for Nonlinear nth-Order Singular Nonlocal Boundary Value Problems |
| title_sort | positive solutions for nonlinear nth order singular nonlocal boundary value problems |
| url | http://dx.doi.org/10.1155/2007/74517 |
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