International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 169-176
doi:10.1155/S0161171293000201
A focal boundary value problem for difference equations
Department of Algebra, Combinatorics, and Analysis, Auburn University, Auburn 36849-5307, Alabama, USA
Received 27 August 1991; Revised 11 April 1992
Copyright © 1993 Cathryn Denny and Darrel Hankerson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The eigenvalue problem in difference equations, (−1)n−kΔny(t)=λ∑i=0k−1pi(t)Δiy(t),
with Δty(0)=0, 0≤i≤k, Δk+iy(T+1)=0, 0≤i<n−k, is examined. Under suitable conditions
on the coefficients pi, it is shown that the smallest positive eigenvalue is a decreasing function of
T. As a consequence, results concerning the first focal point for the boundary value problem with
λ=1 are obtained.