In this paper we consider problems that consist of symplectic difference systems depending on an eigenvalue parameter, together with self-adjoint boundary conditions. Such symplectic difference systems contain as important cases linear Hamiltonian difference systems and also Sturm-Liouville difference equations of second and of higher order. The main result of this paper is an oscillation theorem that relates the number of eigenvalues to the number of generalized zeros of solutions.
M. Bohner et al., "An Oscillation Theorem for Discrete Eigenvalue Problems," Rocky Mountain Journal of Mathematics, Rocky Mountain Mathematics Consortium, Jan 2003.
The definitive version is available at https://doi.org/10.1216/rmjm/1181075460
Mathematics and Statistics
Keywords and Phrases
oscillation; symplectic; Hamiltonian; Discrete systems; eigenvalue problem
International Standard Serial Number (ISSN)
Article - Journal
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