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

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.