Publication details

Solutions with prescribed numbers of focal points of nonoscillatory linear Hamiltonian systems

Investor logo


Year of publication 2023
Type Article in Periodical
Magazine / Source Monatshefte für Mathematik
MU Faculty or unit

Faculty of Science

Keywords Linear Hamiltonian system; Left proper focal point; Right proper focal point; Comparative index; Principal solution Singular; Sturmian separation theorem; Nonoscillation
Description In this paper we present an existence result for conjoined bases of nonoscillatory linear Hamiltonian systems on an unbounded interval, which have prescribed numbers of left and right proper focal points. The result is based on a singular Sturmian separation theorem on an unbounded interval by the authors (2019) and it extends a similar property, which was recently derived for linear Hamiltonian systems on compact interval (2021). At the same time it is new even for completely controllable linear Hamiltonian systems, including higher order Sturm–Liouville differential equations. As the main tools we use the comparative index and properties of the minimal principal solution at infinity, which serves as the reference solution for calculating the numbers of proper focal points. We also provide several examples illustrating the presented theory.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info