Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 82, pp. 1-11.
Title: Positive solutions of a three-point boundary-value problem
on a time scale
Author: Eric R. Kaufmann (Univ. of Arkansas at Little Rock, USA)
Abstract:
Let $\mathbb{T}$ be a time scale such that $0, T \in \mathbb{T}$.
We consider the second order dynamic equation on a time scale
$$\displaylines{
u^{\Delta\nabla}(t) + a(t)f(u(t)) = 0,
\quad t \in (0,T) \cap \mathbb{T},\cr
u(0) = 0, \quad \alpha u(\eta) = u(T),
}$$
where $\eta \in (0, \rho(T)) \cap \mathbb{T}$, and
$0 < \alpha