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.