%0 Journal Article
%T Solution matching for a three-point boundary-value problem on atime scale
%A Martin Eggensperger
%A Eric R. Kaufmann
%A Nickolai Kosmatov
%J Electronic Journal of Differential Equations
%D 2004
%I Texas State University
%X 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 $$displaylines{ y^{DeltaDeltaDelta}(t) = f(t, y(t), y^Delta(t), y^{DeltaDelta}(t)), quad t in [t_1, t_3] cap mathbb{T},cr y(t_1) = y_1, quad y(t_2) = y_2, quad y(t_3) = y_3,. }$$ 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 $[t_2, t_3] cap mathbb{T}$.
%K Time scale
%K boundary-value problem
%K solution matching.
%U http://ejde.math.txstate.edu/Volumes/2004/91/abstr.html