Reid roundabout theorem for symplectic dynamic systems on time scales
| Autoři | |
|---|---|
| Rok publikování | 2001 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Applied Mathematics and Optimization |
| Fakulta / Pracoviště MU | |
| Citace | |
| Obor | Obecná matematika |
| Klíčová slova | time scale; symplectic system; linear Hamiltonian system; quadratic functional; disconjugacy; focal point; principal solution; Riccati equation; Jacobi condition; Legendre condition |
| Popis | The principal aim of this paper is to state and prove the so called Reid roundabout theorem for symplectic dynamic system (S) z\Delta=Stz on an arbitrary time scale T, so that the well known case of differential linear Hamiltonian systems (T=R) and recently developed case of discrete symplectic systems (T=Z) are unified. We list conditions which are equivalent to the positivity of the quadratic functional associated with (S), e.g. disconjugacy (in terms of no focal points of a conjoined basis) of (S), no generalized zeros for vector solutions of (S), the existence of a solution to the corresponding Riccati matrix equation. A certain normality assumption is employed. The result requires treatment of the quadratic functionals both with general and separated boundary conditions. |
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