Publication details

Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems

Investor logo


Year of publication 2019
Type Article in Periodical
Magazine / Source Journal of Differential Equations
MU Faculty or unit

Faculty of Science

Web Full Text
Keywords Linear Hamiltonian system; Proper focal point; Principal solution; Antiprincipal solution; Controllability
Description In this paper we develop new fundamental results in the Sturmian theory for nonoscillatory linear Hamiltonian systems on an unbounded interval. We introduce a new concept of a multiplicity of a focal point at infinity for conjoined bases and, based on this notion, we prove singular Sturmian separation theorems on an unbounded interval. The main results are formulated in terms of the (minimal) principal solutions at both endpoints of the considered interval, and include exact formulas as well as optimal estimates for the numbers of proper focal points of one or two conjoined bases. As a natural tool we use the comparative index, which was recently implemented into the theory of linear Hamiltonian systems by the authors and independently by J. Elyseeva. Throughout the paper we do not assume any controllability condition on the system. Our results turn out to be new even in the completely controllable case.
Related projects:

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

More info