Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 91, pp. 1-7.

Title: Solution matching for a three-point boundary-value 
       problem on atime scale

Authors: Martin Eggensperger(Southeast Arkansas College, Pine Bluff, AR, USA)
         Eric R. Kaufmann (Univ. of Arkansas at Little Rock, AR, USA)
         Nickolai Kosmatov (Univ. of Arkansas at Little Rock, AR, USA)
 
Abstract: 
 Let $\mathbb{T}$ be a time scale such that $t_1, t_2, t_3 \in \mathbb{T}$. 
 We show the existence of a unique solution for the three-point boundary
 value problem
$$\displaylines{
    y^{\Delta\Delta\Delta}(t) = f(t, y(t), y^\Delta(t),
    y^{\Delta\Delta}(t)), \quad t \in [t_1, t_3] \cap \mathbb{T},\cr
    y(t_1) = y_1, \quad y(t_2) = y_2, \quad y(t_3) = y_3\,.
}$$
 We do this by matching a solution to the first equation satisfying a
 two-point boundary conditions on $[t_1, t_2] \cap \mathbb{T}$ 
 with a solution satisfying a two-point boundary conditions on 
 $[t_2, t_3] \cap \mathbb{T}$.
 
Submitted May 14, 2004. Published July 8, 2004.
Math Subject Classifications: 34B10, 34B15, 34G20
Key Words: Time scale; boundary-value problem; solution matching