Eigenvalues of Discrete Second-order Coupled Boundary Value Problems with Sign-changing Weight.

This paper is concerned with discrete secondorder coupled boundary value problems with sign-changing weight. We find that these problems have T real eigenvalues (including the multiplicity). Specifically, the numbers of positive eigenvalues are equal to the number of positive elements in the weight function, and the numbers of negative eigenvalues are equal to the number of negative elements in the weight function. Furthermore, the relationships between the eigenvalues under three different coupled boundary conditions are established. These results extend the relevant existing results of periodic and anti-periodic boundary value problems with sign-changing weight and the coupled boundary value problems with definite weight. [ABSTRACT FROM AUTHOR]