Spectral theory of higher-order discrete vector Sturm–Liouville problems Original Research Article

This paper is concerned with spectral problems of higher-order vector difference equations with self-adjoint boundary conditions, where the coefficient of the leading term may be singular. A suitable admissible function space is constructed so that the corresponding difference operator is self-adjoint in it, and the fundamental spectral results are obtained. Rayleighʹs principles and minimax theorems in two special linear spaces are given. As an application, comparison theorems for eigenvalues of two Sturm–Liouville problems are presented. Especially, the dual orthogonality and multiplicity of eigenvalues are discussed.