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@article{488369,
author = {Hilscher, Roman},
article_number = {5-6},
keywords = {time scale; (continuous and discrete) linear Hamiltonian system; disconjugacy; principal solution; quadratic functional},
language = {eng},
issn = {0895-7177},
journal = {Mathematical and Computer Modelling},
title = {Linear Hamiltonian systems on time scales: positivity of quadratic functionals},
volume = {32},
year = {2000}
}
TY - JOUR ID - 488369 AU - Hilscher, Roman PY - 2000 TI - Linear Hamiltonian systems on time scales: positivity of quadratic functionals JF - Mathematical and Computer Modelling VL - 32 IS - 5-6 SP - 507-527 EP - 507-527 PB - Elsevier Science SN - 08957177 KW - time scale KW - (continuous and discrete) linear Hamiltonian system KW - disconjugacy KW - principal solution KW - quadratic functional N2 - In this work we consider a linear Hamiltonian system (H)
x\Delta = At x\sigma + Bt u,
u\Delta = -Ct x\sigma - AtT u on an arbitrary time scale T, which allows (among others)
- to treat both continuous and discrete linear Hamiltonian systems (as the special cases for T=R and T=Z) within one theory;
- to explain the discrepancies between these two theories while studying systems of the form (H).
As a main result we prove that disconjugacy of the system (H) is a sufficient condition for positive definiteness of the quadratic functional associated with (H). The principal tool is the Picone identity on T. We derive also the corresponding Wronskian identity, Riccati equation in this general setting on time scales. ER - HILSCHER, Roman. Linear Hamiltonian systems on time scales: positivity of quadratic functionals. \textit{Mathematical and Computer Modelling}. Elsevier Science, 2000, roč.~32, 5-6, s.~507-527, 20 s. ISSN~0895-7177.
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