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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 a 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, roč.~43, MAY, s.~114-119. ISSN~0893-9659. Dostupné z: https://dx.doi.org/10.1016/j.aml.2014.12.003.
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