On general Sturmian theory for abnormal linear Hamiltonian systems

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Authors	ŠIMON HILSCHER Roman
Year of publication	2011
Type	Article in Proceedings
Conference	Proceedings of the 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
MU Faculty or unit	Faculty of Science
Citation
Web	http://aimsciences.org/journals/contentsListPro.jsp?pubID=469
Doi	http://dx.doi.org/10.3934/proc.2011.2011.684
Field	General mathematics
Keywords	Linear Hamiltonian system; Sturmian separation theorem; Sturmian comparison theorem; proper focal point; conjoined basis; controllability; normality
Attached files	dcdss_procsturm.pdf
Description	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.
Related projects:	Mathematical structures and their physical applications Oscillation and spectral theory of differential and difference systems