 
Summary: A 2nTH ORDER LINEAR
DIFFERENCE EQUATION
Doug Anderson
Department of Mathematics and Computer Science, Concordia College
Moorhead, MN 56562, USA
ABSTRACT: We give a formulation of generalized zeros and (n, n)disconjugacy
for even order formally selfadjoint scalar linear difference equations. Sign conditions
on the coefficient functions ensure (n, n)disconjugacy. This and additional results
are obtained with the use of an associated nonlinear operator.
AMS Subject Classification. 39A10.
1 INTRODUCTION
In this paper we will be concerned with the 2nthorder linear difference equation
n
i=0
i
ri(t  i)i
y(t  i) = 0 (1)
for t in the discrete interval [a, ) {a, a + 1, a + 2, . . .}, where ri(t) is realvalued
on [a + n  i, ) for 0 i n, and
rn(t) > 0 (2)
