Smoothness of Solutions of Conjugate Boundary-Value Problems on a Measure Chain

SMOOTHNESS OF SOLUTIONS OF CONJUGATE BOUNDARY-VALUE PROBLEMS ON A MEASURE CHAIN.

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

Electronic Journal of Differential Equations, 2000 (2000), No. 54, 1-10.

ABSTRACT: In this paper we consider the n-th order D-differential equation (often refered to as a differential equation on a measure chain)

u^D_n (t) = f (t, u(s(t)), . . . , u^{D_{n - 1}}(s(t)) ) satisfying n-point conjugate boundary conditions. We show that solutions depend continuously and smoothly on the boundary values.

AMS (MOS) subject classification 34B15, 34B99, 39A10, 34A99.

Key Words: Measure chain, initial-value problem, boundary-value problem.

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