On general Sturmian theory for abnormal linear Hamiltonian systems

Roman Šimon Hilscher

doi:10.3934/proc.2011.2011.684

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2011, Volume 2011: 684-691. Doi: 10.3934/proc.2011.2011.684 open access

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On general Sturmian theory for abnormal linear Hamiltonian systems

Roman Šimon Hilscher^1,

1.
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-61137 Brno

Received: June 30, 2010

Revised: January 31, 2011

Published: August 2017

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Abstract

In this paper we discuss oscillation theory for linear Hamiltonian systems for which we do not impose the controllability (or equivalently normality) assumption. Based on the Sturmian separation and comparison theorems on a compact interval, derived earlier by the author for these systems, we classify them as oscillatory or nonoscillatory. Moreover, we provide comparison theorems for such oscillatory and nonoscillatory systems. One of the goals of this paper is to provide several examples illustrating this new theory.

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Mathematics Subject Classification: Primary: 34C10; Secondary: 34B24.

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