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

We consider the discrete right definite Sturm–Liouville problems−Δ(p(t−1)Δy(t−1))+q(t)y(t)=λm(t)y(t),t∈[1,T]Z,(a0λ+b0)y(0)=(c0λ+d0)Δy(0),(a1λ+b1)y(T+1)=(c1λ+d1)∇y(T+1), where [1,T]Z={1,2,⋯,T}[1,T]Z={1,2,⋯,T}, m(t)>0m(t)>0 for t∈[1,T]Zt∈[1,T]Z, (−1)iδi≤0(−1)iδi≤0, where δi=aidi−biciδi=aidi−bici for i=0,1i=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.