Eigenvalue comparisons for a class of boundary value problems of second order difference equations

We consider the boundary value problem for second order difference equationΔ(ri-1Δyi-1)-biyi+λaiyi=0,1⩽i⩽n,y0-τy1=yn+1-δyn=0.In this study we do not require the positiveness of {ak}k=1n. We focus on the structure of eigenvalues of this problem and comparisons of all eigenvalues as the coefficients {ai}i=1n, {bi}i=1n, {ri}i=0n and the parameters τ, δ change.