 
Summary: DISCRETE THIRDORDER THREEPOINT RIGHT FOCAL
BOUNDARY VALUE PROBLEMS
DOUGLAS R. ANDERSON
Abstract. We are concerned with the discrete rightfocal boundary value
problem 3x(t) = f(t, x(t + 1)), x(t1) = x(t2) = 2x(t3) = 0, and the
eigenvalue problem 3x(t) = a(t)f(x(t + 1)) with the same boundary condi
tions, where t1 < t2 < t3. Under various assumptions on f, a and we prove
the existence of positive solutions of both problems by applying a fixed point
theorem.
1. Introduction
In this paper, we are concerned with the existence of positive solutions to the
discrete thirdorder threepoint eigenvalue problem:
3
x(t) = a(t)f(x(t + 1)) for all t [t1, t3  1] (1)
x(t1) = x(t2) = 2
x(t3) = 0,
and the boundary value problem
3
x(t) = f(t, x(t + 1)) for all t [t1, t3  1] (2)
x(t1) = x(t2) = 2
