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Zbl 1140.34313
Liang, Ruixi; Peng, Jun; Shen, Jianhua
Positive solutions to a generalized second order three-point boundary value problem.
(English)
[J] Appl. Math. Comput. 196, No. 2, 931-940 (2008). ISSN 0096-3003

Summary: By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to the nonlinear second order three-point boundary value problem $$y''(t)+a(t)f(y(t))=0,\quad 0<t<T,\quad y(0)=\beta y(\eta),\quad y(T)=\alpha y(n),$$ where $0<\eta<T$, $0<\alpha<\frac T\eta$, $0<\beta<\frac{T-\alpha\eta}{T-\eta}$ are given constants. As an application, we also present some examples to illustrate our results.
MSC 2000:
*34B10 Multipoint boundary value problems
34B18 Positive solutions of nonlinear boundary value problems
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: positive solutions; three-point boundary value problem; Krasnoselskii fixed point theorem

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