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

J 2015

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

DOŠLÝ, Ondřej and Julia ELYSEEVA

Basic information

Original name

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

Authors

DOŠLÝ, Ondřej (203 Czech Republic, guarantor, belonging to the institution) and Julia ELYSEEVA (643 Russian Federation)

Edition

Applied Mathematical Letters, 2015, 0893-9659

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 1.659

RIV identification code

RIV/00216224:14310/15:00080632

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1016/j.aml.2014.12.003

UT WoS

000350085500020

Keywords in English

Discrete eigenvalue problem; Hamiltonian difference system; oscillation theorem; finite eigenvalue; comparative index

Abstract

V originále

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.

Links

GAP201/10/1032, research and development project

Name: Diferenční rovnice a dynamické rovnice na ,,time scales'' III (Acronym: Difrov)

Investor: Czech Science Foundation

Citovat

DOŠLÝ, Ondřej and Julia ELYSEEVA. Discrete oscillation theorems and weighted focal points for Hamiltonian difference systems with nonlinear dependence on a spectral parameter. 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.

@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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