Eigenvalues of discrete Sturm-Liouville problems with eigenparameter dependent boundary conditions

We consider the discrete right definite Sturm-Liouville problems -Delta(p(t - 1)Delta y(t - 1)) + q(t)y(t) = lambda m(t)y(t), t epsilon [1, T]z, (a(0)lambda + b(0))y(0) = (c(0 lambda) + d(0))Delta y(0), (a(1)lambda)) + b(1))y(T + 1) = (c(1 lambda) + d(1))del y(T + 1), where [1, T]z = {1, 2,, T}, m(t) > 0 for t epsilon [1, T]z, (-1)(i) delta(i) <= 0, where delta(i) = a(i)d(i) - b(i)c(i) for i = 0, 1. We obtain the existence of the eigenvalues, the sign-changing times of the eigenfunctions and the interlacing results of the eigenvalues of the above problem, the Dirichlet problem and the Neumann problem. (C) 2016 Elsevier Inc. All rights reserved.