Electron. J. Diff. Eqns., Vol. 2004(2004), No. 91, pp. 1-7.

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

Martin Eggensperger, Eric R. Kaufmann, Nickolai Kosmatov

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.

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  Martin Eggensperger
General Studies, Southeast Arkansas College
Pine Bluff, Arkansas, USA
email: meggensperger@seark.edu
Eric R. Kaufmann
Department of Mathematics and Statistics
University of Arkansas at Little Rock
Little Rock, Arkansas 72204-1099, USA
email: erkaufmann@ualr.edu
  Nickolai Kosmatov
Department of Mathematics and Statistics
University of Arkansas at Little Rock
Little Rock, Arkansas 72204-1099, USA
email: nxkosmatov@ualr.edu

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