Summary: Three Positive Solutions to a Discrete Focal Boundary
Department of Mathematics and Computer Science, Concordia College
Moorhead, MN 56562
R. Avery and A. Peterson
Department of Mathematics and Statistics, University of Nebraska-Lincoln
Lincoln, NE 68588-0323
ravery@@math.unl.edu and apeterso@@math.unl.edu
We are concerned with the discrete focal boundary value problem 3x(t-k) = f(x(t)),
x(a) = x(t2) = 2x(b + 1) = 0. Under various assumptions on f and the integers a, t2,
and b we prove the existence of three positive solutions of this boundary value problem.
To prove our results we use fixed point theorems concerning cones in a Banach space.
Key words: difference equations, Green's function, fixed points.
AMS Subject Classification: 39A10.
In this section we will state the two fixed point theorems that we will use to prove our main
results. First we will make a few definitions.