Eigenvalue Comparisons for Second Order Difference Equations with Periodic and Antiperiodic Boundary Conditions

Authors

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

Department

Mathematics

Document Type

Article

Publication Date

5-2008

Abstract

We consider a class of boundary value problems of the second order difference equation Δ(r_i-1Δ y_i-1)-b _iy_i+λa_iy_i = 0, 1 ≤ i ≤ n, y₀ = α y_n, y_n+1 = α y ₁. The class of problems considered includes those with antiperiodic, Dirichlet, and periodic boundary conditions. We focus on the structure of eigenvalues of this class of problems and comparisons of all eigenvalues as the coefficients {a_i}_i=1ⁿ,{b_i} _i=1ⁿ, and {r_i}_i=0ⁿ change