| Issue |
EPJ Web Conf.
Volume 248, 2021
V International Conference “Modeling of Nonlinear Processes and Systems“ (MNPS-2020)
|
|
|---|---|---|
| Article Number | 01002 | |
| Number of page(s) | 6 | |
| Section | Mathematical Models in Natural Sciences | |
| DOI | https://doi.org/10.1051/epjconf/202124801002 | |
| Published online | 26 April 2021 | |
https://doi.org/10.1051/epjconf/202124801002
The Oscillation Numbers and the Abramov Method of Spectral Counting for Linear Hamiltonian Systems
Department of Applied Mathematics, Moscow State Technological University “STANKIN”, RU-127055, Moscow, Russia
* Corresponding author: elyseeva@gmail.com
Published online: 26 April 2021
In this paper we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. For the Hamiltonian problems we do not assume any controllability and strict normality assumptions which guarantee that the classical eigenvalues of the problems are isolated. We also omit the Legendre condition for their Hamiltonians. We show that the Abramov method of spectral counting can be modified for the more general case of finite eigenvalues of the Hamiltonian problems and then the constructive ideas of the Abramov method can be used for stable calculations of the oscillation numbers and finite eigenvalues of the Hamiltonian problems.
© The Authors, published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.