R.Simon Hilscher

On general Sturmian theory for abnormal linear Hamiltonian systems

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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Last change: February 1, 2011. (c) Roman Simon Hilscher