P. Sepitka, R. Simon Hilscher

Sturmian comparison theorems for completely controllable linear Hamiltonian systems in singular case

Abstract

In this paper we consider two linear Hamiltonian differential systems on an open unbounded interval. We assume that the systems are completely controllable and satisfy the Sturmian majorant condition and the Legendre condition. We derive a singular Sturmian comparison theorem for the case when the minorant system has a solution, which is principal at both endpoints of the considered interval. The main result is new even for the second order differential equations and it generalizes the singular comparison theorem obtained by Aharonov and Elias (2010). We illustrate our new theory by several examples.


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Last change: 09.03.2020. (c) Roman Simon Hilscher