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