Geodesic
Solution matching for a three-point boundary-value problem on a time scale
Electronic journal of differential equations, Tome 2004 (2004)
Let

$\displaylines{ y^{\Delta\Delta\Delta}(t) = f(t, y(t), y^\Delta(t), y^{\Delta\Delta}(t)), \quad t \in [t_1, t_3] \cap \mathbb{T},\cr y(t_1) = y_1, \quad y(t_2) = y_2, \quad y(t_3) = y_3\,. }$

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 $[t_2, t_3] \cap \mathbb{T}$.
Classification : 34B10, 34B15, 34G20
Keywords: time scale, boundary-value problem, solution matching 
@article{EJDE_2004__2004__a135,
     author = {Eggensperger,  Martin and Kaufmann,  Eric R. and Kosmatov,  Nickolai},
     title = {Solution matching for a three-point boundary-value problem on a time scale},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1062.34010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a135/}
}
TY  - JOUR
AU  - Eggensperger,  Martin
AU  - Kaufmann,  Eric R.
AU  - Kosmatov,  Nickolai
TI  - Solution matching for a three-point boundary-value problem on a time scale
JO  - Electronic journal of differential equations
PY  - 2004
VL  - 2004
UR  - http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a135/
LA  - en
ID  - EJDE_2004__2004__a135
ER  - 
%0 Journal Article
%A Eggensperger,  Martin
%A Kaufmann,  Eric R.
%A Kosmatov,  Nickolai
%T Solution matching for a three-point boundary-value problem on a time scale
%J Electronic journal of differential equations
%D 2004
%V 2004
%U http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a135/
%G en
%F EJDE_2004__2004__a135
Eggensperger,  Martin; Kaufmann,  Eric R.; Kosmatov,  Nickolai. Solution matching for a three-point boundary-value problem on a time scale. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a135/