Smoothness of Solutions of an <I>n</I>-point Right Focal Boundary Value Problem on a Time Scale

SMOOTHNESS OF SOLUTIONS OF AN n-POINT RIGHT FOCAL BOUNDARY VALUE PROBLEM ON A TIME SCALE.

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

Submitted.

ABSTRACT: In this paper we consider the n^th order D-differential equation (often referred to as a differential equation on a time scale)

u^Dⁿ (t) = f (t, u(s(t)), . . . , u^{D^{n - 1}}(s(t)), l ) satisfying n-point right focal boundary conditions. We give sufficient conditions under which solutions depend continuously and smoothly on the boundary values and the parameter.

AMS (MOS) subject classification 34B15, 34G20, 39A05, 39A13.

Key Words: Time Scale, initial value problem, boundary value problem.

Return to research page.