Generalized oscillation theorems for symplectic difference systems with nonlinear dependence on spectral parameter

Julia Elyseeva

Applied Mathematics and Computation, 2015, vol. 251, issue C, 92-107

Abstract: In this paper we generalize oscillation theorems for discrete symplectic eigenvalue problems with nonlinear dependence on spectral parameter recently proved by R. Šimon Hilscher and W. Kratz under the assumption that the block Bk(λ) of the symplectic coefficient matrices located in the right upper corner has a constant image for all λ∈R. In our version of the discrete oscillation theorems we avoid this assumption admitting that rankBk(λ) is a piecewise constant function of the spectral parameter λ. Assuming a monotonicity condition for the symplectic coefficient matrices we show that spectrum of symplectic eigenvalue problems with the Dirichlet boundary conditions is bounded from below iff so is the number of jump discontinuities of rankBk(λ).

Keywords: Discrete eigenvalue problem; Symplectic difference system; Oscillation theorem; Finite eigenvalue; Comparative index (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300314015744
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:251:y:2015:i:c:p:92-107

DOI: 10.1016/j.amc.2014.11.042

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().