Eigenvalue Comparisons for a Class of Boundary Value Problems of Second Order Difference Equations

Authors

Jun Ji, Kennesaw State UniversityFollow
Bo Yang, Kennesaw State UniversityFollow

Department

Mathematics

Document Type

Article

Publication Date

1-1-2007

Abstract

We consider the boundary value problem for second order difference equation Δ(r_i-1Δy_i-1) - b_iy_i + λa_iy_i = 0, 1 ≤ i ≤ n, y₀ - τy₁ = y_n+1 - δy_n = 0. In this study we do not require the positiveness of {a_k}ⁿ_k=1. We focus on the structure of eigenvalues of this problem and comparisons of all eigenvalues as the coefficients {a_i}ⁿ_i=1, {b_i}ⁿ_i=1, {r_i}ⁿ_i=0 and the parameters τ, δ change.