Electron. J. Diff. Eqns., Vol. 2003(2003), No. 82, pp. 1-11.

Positive solutions of a three-point boundary-value problem on a time scale

Eric R. Kaufmann

Abstract:
Let $\mathbb{T}$ be a time scale such that $0, T \in \mathbb{T}$. We consider the second order dynamic equation on a time scale
$$\displaylines{ u^{\Delta\nabla}(t) + a(t)f(u(t)) = 0, \quad t \in (0,T) \cap \mathbb{T},\cr u(0) = 0, \quad \alpha u(\eta) = u(T), }$$
where $\eta \in (0, \rho(T)) \cap \mathbb{T}$, and $0 < \alpha <T/\eta$. We apply a cone theoretic fixed point theorem to show the existence of positive solutions.

Submitted May 9, 2003. Published August 9, 2003.
Math Subject Classifications: 34B10, 34B15, 34G20.
Key Words: Time scale, cone, boundary-value problem, positive solutions.

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Eric R. Kaufmann
Department of Mathematics and Statistics
University of Arkansas at Little Rock
Little Rock, Arkansas 72204-1099, USA
email: erkaufmann@ualr.edu

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