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Zbl 1047.34015
Kaufmann, Eric R.
Positive solutions of a three-point boundary-value problem on a time scale.
(English)
[J] Electron. J. Differ. Equ. 2003, Paper No. 82, 11 p., electronic only (2003). ISSN 1072-6691/e

Let {\bf T} be a time scale such that $0,T\in {\bold T}$. 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 $$u^{\nabla\nabla}(t)+a(t)f(u(t))=0, \quad t\in (0,T)\cap {\bold T},$$ $$u(0)=0, \quad \alpha u(\eta)=y(T),$$ where $\eta\in (0,\rho(T))\cap {\bold T}$, and $0<\alpha<T/\eta.$
[Patricia J. Y. Wong (Singapore)]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
39A12 Discrete version of topics in analysis

Keywords: Time scale; boundary value problem; positive solutions.

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