An Oscillation Theorem for Discrete Eigenvalue Problems

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Ondřej Došlý
Werner Kratz

Abstract

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Keywords and Phrases

oscillation; symplectic; Hamiltonian; Discrete systems; eigenvalue problem

International Standard Serial Number (ISSN)

0035-7596

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2003 Rocky Mountain Mathematics Consortium, All rights reserved.

Publication Date

01 Jan 2003