Publication details
Oscillation theorems for symplectic difference systems
| Authors | |
|---|---|
| Year of publication | 2007 |
| Type | Article in Periodical |
| Magazine / Source | J. Difference Equ. Appl. |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Local oscillation theorem; global oscillation theorem; discrete eigenvalue problem; symplectic difference system;focal point; conjoined basis; principal solution |
| Description | We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same problem was treated and an essential ingredient was to establish the concept of the multiplicity of a focal point. But there was still a rather restrictive condition needed, which is eliminated here by using the concept of finite eigenvalues (or zeros) from the theory of matrix pencils. |
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