Eigenvalue Comparisons for Second Order Difference Equations with Neumann Boundary Conditions



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The boundary value problem for second order difference equationΔ (ri - 1 Δ yi - 1) - bi yi + λ ai yi = 0, 1 ≤ i ≤ n y0 - τ y1 = yn + 1 - δ yn = 0with δ, τ ∈ [0, 1] and τ + δ ≠ 2 was recently discussed in Ji and Yang (2007) [J. Ji, B. Yang, Eigenvalue comparisons for a class of boundary value problems of second order difference equations, Linear Algebra Appl. 420 (1) (2007) 218-227]. In this paper we extend our earlier results to the second order difference equations with Neumann boundary conditions (the case of τ = δ = 1). As in Ji and Yang (2007) mentioned above, we will also focus on the structure of its eigenvalues and comparisons of all eigenvalues as the coefficients {ai}, {bi}, and {ri} change.