Discrete oscillation theorems and weighted focal points for Hamiltonian difference systems with nonlinear dependence on a spectral parameter

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Authors

DOŠLÝ Ondřej ELYSEEVA Julia

Year of publication 2015
Type Article in Periodical
Magazine / Source Applied Mathematical Letters
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1016/j.aml.2014.12.003
Field General mathematics
Keywords Discrete eigenvalue problem; Hamiltonian difference system; oscillation theorem; finite eigenvalue; comparative index
Description 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.
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