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@article{1215488,
author = {Došlý, Ondřej and Elyseeva, Julia},
article_number = {MAY},
doi = {http://dx.doi.org/10.1016/j.aml.2014.12.003},
keywords = {Discrete eigenvalue problem; Hamiltonian difference system; oscillation theorem; finite eigenvalue; comparative index},
language = {eng},
issn = {0893-9659},
journal = {Applied Mathematical Letters},
title = {Discrete oscillation theorems and weighted focal points for Hamiltonian difference systems with nonlinear dependence on a spectral parameter},
volume = {43},
year = {2015}
}
TY - JOUR
ID - 1215488
AU - Došlý, Ondřej - Elyseeva, Julia
PY - 2015
TI - Discrete oscillation theorems and weighted focal points for Hamiltonian difference systems with nonlinear dependence on a spectral parameter
JF - Applied Mathematical Letters
VL - 43
IS - MAY
SP - 114-119
EP - 114-119
SN - 08939659
KW - Discrete eigenvalue problem
KW - Hamiltonian difference system
KW - oscillation theorem
KW - finite eigenvalue
KW - comparative index
N2 - In this paper we generalize oscillation theorems for discrete Hamiltonian eigenvalue problems with nonlinear dependence on the spectral parameter. In our version of the discrete oscillation theorems, we incorporate the case when the block B of the discrete Hamiltonian H has nonconstant rank with respect to the spectral parameter. We introduce a new notion of weighted focal points for conjoined bases of the Hamiltonian difference systems and we show that the number of weighted focal points plays the role of the classical number of focal points in the discrete oscillation theorems for the Hamiltonian spectral problems with the nonconstant rank of B.
ER -
DOŠLÝ, Ondřej and Julia ELYSEEVA. Discrete oscillation theorems and weighted focal points for Hamiltonian difference systems with nonlinear dependence on a spectral parameter. \textit{Applied Mathematical Letters}. 2015, vol.~43, MAY, p.~114-119. ISSN~0893-9659. Available from: https://dx.doi.org/10.1016/j.aml.2014.12.003.
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