Comparison theorems for conjoined bases of linear Hamiltonian systems without monotonicity
| Autor: | Julia Elyseeva |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
010505 oceanography General Mathematics 010102 general mathematics Comparison results Monotonic function Differential systems 01 natural sciences Hamiltonian system Combinatorics symbols.namesake symbols 0101 mathematics Hamiltonian (quantum mechanics) Legendre polynomials 0105 earth and related environmental sciences Symplectic geometry |
| Zdroj: | Monatshefte für Mathematik. 193:305-328 |
| ISSN: | 1436-5081 0026-9255 |
| DOI: | 10.1007/s00605-020-01378-8 |
| Popis: | In this paper we generalize comparison results for conjoined bases $$Y(t),{{\hat{Y}}}(t)$$ of two linear Hamiltonian differential systems proved by Elyseeva (J Math Anal Appl 444:1260–1273, 2016). In our consideration we do not impose classical monotonicity assumptions such that the majorant condition $${\mathcal {H}}(t)-\hat{\mathcal {H}}(t)\ge 0$$ for their Hamiltonians $${\mathcal {H}}(t), \hat{\mathcal {H}}(t)$$ and the Legendre conditions for $${\mathcal {H}}(t),\hat{\mathcal {H}}(t)$$ . Our new comparison theorems are presented in terms of the so-called oscillation numbers associated with $$Y(t), {{\hat{Y}}}(t),$$ and the transformed conjoined basis $${\hat{Z}}^{-1}(t)Y(t)$$ , where $${\hat{Z}}(t)$$ is a symplectic fundamental solution matrix of the Hamiltonian system with the Hamiltonian $$\hat{\mathcal {H}}(t)$$ . The consideration is based on the comparative index theory applied to the continuous case. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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