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A 2nTH ORDER LINEAR DIFFERENCE EQUATION
 

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 self-adjoint 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 2nth-order 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 real-valued
on [a + n - i, ) for 0 i n, and
rn(t) > 0 (2)

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics