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@inproceedings{488375,
author = {Hilscher, Roman},
address = {Amsterdam},
booktitle = {Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations},
keywords = {time scale; linear Hamiltonian system; disconjugacy; generalized zero; quadratic functional},
language = {eng},
location = {Amsterdam},
isbn = {90-5699-688-6},
pages = {181-188},
publisher = {Gordon and Breach},
title = {On disconjugacy for vector linear Hamiltonian systems on time scales},
year = {2000}
}
TY - JOUR
ID - 488375
AU - Hilscher, Roman
PY - 2000
TI - On disconjugacy for vector linear Hamiltonian systems on time scales
PB - Gordon and Breach
CY - Amsterdam
SN - 9056996886
KW - time scale
KW - linear Hamiltonian system
KW - disconjugacy
KW - generalized zero
KW - quadratic functional
N2 - In this work we present a unified treatment of continuous and discrete vector linear Hamiltonian systems on a general time scale T, with the matrix Bt not necessarily invertible. This contains as special cases the Sturm-Liouville differential and difference equations of higher order. We define generalized zeros for vector solutions (x,u) of the Hamiltonian system. From this we read off the corresponding definition of generalized zero points for solutions of the Sturm-Liouville equations, so that the well known continuous case (T=R) and recently developed discrete one (T=Z) are unified. We show that disconjugacy of the equation implies positivity of the corresponding quadratic functional.
ER -
HILSCHER, Roman. On disconjugacy for vector linear Hamiltonian systems on time scales. In \textit{Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations}. Amsterdam: Gordon and Breach, 2000, s.~181-188. ISBN~90-5699-688-6.
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