 
Summary: Dynamic Systems and Applications xx (200x) xx
EXTENSION OF A SECONDORDER MULTIPOINT PROBLEM
TO TIME SCALES
DOUGLAS R. ANDERSON
Department of Mathematics, Concordia College, Moorhead, MN 56562 USA
ABSTRACT. We extend a secondorder multipoint nonlinear boundary value problem on the
unit interval to the general timescale problem
x
(t) + a(t)g(x(t)) = 0, t (t1, tn) T
x(t1) = 0, x(tn) 
n1
i=2
ix(ti) = ,
where T is a time scale; t1 < t2 < · · · < tn are points in T with t1 T, tn T
, and tn1 < (tn);
and , i > 0 for i = 2, · · · , n  1. Then, using the Schauder fixed point theorem, we establish the
existence of a positive solution if (0, ) for some > 0, and no positive solution for > .
AMS (MOS) Subject Classification. 39A10, 34B10.
1. PRELIMINARIES ABOUT TIME SCALES
Any arbitrary nonempty closed subset of the set of real numbers R can serve as
