An Oscillation Theorem for Discrete Eigenvalue Problems

Martin Bohner; Ondřej Došlý; Werner Kratz

doi:10.1216/rmjm/1181075460

An Oscillation Theorem for Discrete Eigenvalue Problems

Martin Bohner
, Ondřej Došlý
, Werner Kratz

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Rocky Mountain Journal of Mathematics
DOIs	https://doi.org/10.1216/rmjm/1181075460
State	Published - Jan 1 2003

Keywords

Discrete systems
Hamiltonian
eigenvalue problem
oscillation
symplectic

Disciplines

Mathematics
Statistics and Probability

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10.1216/rmjm/1181075460License: Unspecified

An Oscillation Theorem for Discrete Eigenvalue ProblemsFinal published version, 294 KBLicense: Unspecified

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title = "An Oscillation Theorem for Discrete Eigenvalue Problems",

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.",

keywords = "Discrete systems, Hamiltonian, eigenvalue problem, oscillation, symplectic",

author = "Martin Bohner and Ond{\v r}ej Do{\v s}l{\'y} and Werner Kratz",

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doi = "10.1216/rmjm/1181075460",

language = "American English",

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AU - Došlý, Ondřej

AU - Kratz, Werner

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N2 - 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.

AB - 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.

KW - Discrete systems

KW - Hamiltonian

KW - eigenvalue problem

KW - oscillation

KW - symplectic

UR - https://scholarsmine.mst.edu/math_stat_facwork/166

U2 - 10.1216/rmjm/1181075460

DO - 10.1216/rmjm/1181075460

M3 - Article

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

ER -

An Oscillation Theorem for Discrete Eigenvalue Problems

Abstract

Keywords

Disciplines

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