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Zbl 1148.34015
Hao, Xin'an; Liu, Lishan; Wu, Yonghong
Positive solutions for nonlinear $n$th-order singular nonlocal boundary value problems.
(English)
[J] Bound. Value Probl. 2007, Article ID 74517, 10 p. (2007). ISSN 1687-2770/e

Summary: We study the existence and multiplicity of positive solutions for a class of $n$th-order singular nonlocal boundary value problems $$u^{(n)}(t)+a(t)f(t,u) = 0,\quad t\in (0,1),\quad u(0) = 0,\quad u'(0) = 0,\dots,u^{(n-2)}(0) =0,\quad \alpha u(\eta) =u(1),$$ where $0<\eta <1$, $0<\alpha\eta^{n-1}<1$. 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.
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B10 Multipoint boundary value problems
34B16 Singular nonlinear boundary value problems

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