 
Summary: AN EVENORDER THREEPOINT BOUNDARY VALUE PROBLEM ON
TIME SCALES
DOUGLAS R. ANDERSON AND RICHARD I. AVERY
Abstract. We study the evenorder dynamic equation (1)n
x( )n
(t) = h(t)f(x(t)), t
[a, c] satisfying the boundary conditions x( )i
(a) = 0 and x( )i
(c) = x( )i
(b) for 0 i
n  1. The three points a, b, c are from a time scale T, where 0 < (b  a) < c  a for b (a, c),
> 0, f is a positive function, and h is a nonnegative function that is allowed to vanish on
some subintervals of [a, c] of the time scale.
1. introduction
In this paper we are concerned with the evenorder dynamic equation
(1) (1)n
x( )n
(t) = h(t)f(x(t)), t [a, c], n N,
satisfying the threepoint boundary conditions
(2) x( )i
