# zbMATH — the first resource for mathematics

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
##### Keywords:
Time scale; boundary value problem; positive solutions.
Full Text: