On general Sturmian theory for abnormal linear Hamiltonian systems

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2011, 2011(Special): 684-691. doi: 10.3934/proc.2011.2011.684

On general Sturmian theory for abnormal linear Hamiltonian systems

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

Received July 2010 Revised February 2011 Published October 2011

Abstract
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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.

Keywords: Linear Hamiltonian system, conjoined basis, Sturmian separation theorem, Sturmian comparison theorem, proper focal point, controllability, normality.

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

Citation: Roman Šimon Hilscher. On general Sturmian theory for abnormal linear Hamiltonian systems. Conference Publications, 2011, 2011 (Special) : 684-691. doi: 10.3934/proc.2011.2011.684

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