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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 1, Pages 169-176
http://dx.doi.org/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 Hindawi Publishing Corporation. 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)nkΔny(t)=λi=0k1pi(t)Δiy(t), with Δty(0)=0, 0ik, Δk+iy(T+1)=0, 0i<nk, 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.