Geodesic
Positive solutions of a three-point boundary-value problem on a time scale
Electronic journal of differential equations, Tome 2003 (2003)
Let

$\displaylines{ u^{\Delta\nabla}(t) + a(t)f(u(t)) = 0, \quad t \in (0,T) \cap \mathbb{T},\cr u(0) = 0, \quad \alpha u(\eta) = u(T), }$

where $\eta \in (0, \rho(T)) \cap \mathbb{T}$, and $0 \alpha $. We apply a cone theoretic fixed point theorem to show the existence of positive solutions.
Classification : 34B10, 34B15, 34G20
Keywords: time scale, cone, boundary-value problem, positive solutions 
@article{EJDE_2003__2003__a180,
     author = {Kaufmann,  Eric R.},
     title = {Positive solutions of a three-point boundary-value problem on a time scale},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1047.34015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a180/}
}
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Kaufmann,  Eric R. Positive solutions of a three-point boundary-value problem on a time scale. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a180/