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Zbl 1032.34020
Liu, Bing
Positive solutions of a nonlinear three-point boundary value problem.
(English)
[J] Appl. Math. Comput. 132, No.1, 11-28 (2002). ISSN 0096-3003

Here, by using Krasnoselskii's fixed-point theorem in a cone, the author studies the existence of single and multiple positive solutions to the following three-point boundary value problem $$y''(t)+a(t)f(y(t))=0, \quad 0<t<1,\qquad y'(0)=0, \ y'(1)=\beta y(\eta),$$ with $0<\beta <1$, $0<\eta <1,$ $f\in C([0,\infty), [0,\infty)),$ $a\in C([0,1], [0,\infty))$ and $a(t_0)>0$ for some $t_0\in [0,1].$ Some examples are also given to illustrate the results.
[Sotiris K.Ntouyas (Ioannina)]
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B10 Multipoint boundary value problems

Keywords: Positive solutions; Krasnoselskii's fixed-point theorem; Cone

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