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Positive solutions to a generalized second order three-point boundary value problem. (English) Zbl 1140.34313
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:
34B10Nonlocal and multipoint boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
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References:
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