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 |
| Summary: | 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. |
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| ISSN: | 1687-2762 1687-2770 |