Electron. J. Diff. Eqns., Vol. 2000(2000), No. 54, pp. 1-10.

Smoothness of solutions of conjugate boundary-value problems on a measure chain

Eric R. Kaufmann

Abstract:
In this paper we consider the n-th order $\Delta$-differential equation (often refered to as a differential equation on a measure chain)
$$u^{\Delta_n}(t) = f(t, u(\sigma(t)),\dots, u^{\Delta_{n-1}}(\sigma(t)))$$
satisfying n-point conjugate boundary conditions. We show that solutions depend continuously and smoothly on the boundary values.

Submitted June 27, 2000. Published July 14, 2000.
Math Subject Classifications: 34B15, 34B99, 39A10, 34A99.
Key Words: Measure chain, initial-value problem, boundary-value problem

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

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