On general Sturmian theory for abnormal linear Hamiltonian systems
| Authors | |
|---|---|
| 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 | |
| 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 | |
| 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. |
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