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.