In this paper we study a boundary value problem for a discrete elliptic equation. The focus will be on the structure of the spectrum of this problem and the existence of a positive eigenvector corresponding to the smallest eigenvalue. Comparison results for the eigenvalues are also established as the coefficients of the problem changes.
Communications in Applied Analysis
Ji, J., & Yang, B. (2008). Eigenvalue comparisons for boundary value problems of the discrete elliptic equation. Communications in Applied Analysis, 12(2), 189-198.