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
  $0 < \alpha <T/\eta$. We apply a cone theoretic fixed point theorem
  to show the existence of positive solutions.
 
Submitted May 9, 2003. Published August 9, 2003.
Math Subject Classifications: 34B10, 34B15, 34G20.
Key Words: Time scale; cone; boundary-value problem; positive solutions.