Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 54, pp. 1-10.
Title: Smoothness of solutions of conjugate boundary-value problems
on a measure chain
Author: Eric R. Kaufmann (Univ. of Arkansas at Little Rock, USA)
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.