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Positive solutions of a three-point boundary-value problem on a time scale. (English) Zbl 1047.34015
Let T be a time scale such that \(0,T\in {\mathbf T}\). The author utilizes a theoretic fixed-point theorem in a cone to show the existence of positive solutions of the second-order boundary value problem \[ u^{\nabla\nabla}(t)+a(t)f(u(t))=0, \quad t\in (0,T)\cap {\mathbf T}, \]
\[ u(0)=0, \quad \alpha u(\eta)=y(T), \] where \(\eta\in (0,\rho(T))\cap {\mathbf T}\), and \(0<\alpha<T/\eta.\)

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
39A12 Discrete version of topics in analysis
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