Ondrej Dosly, Roman Hilscher, Department of Mathematics, Faculty of Science, Masaryk University Brno, Janackovo nam. 2a, 662 95 Brno, Czech Republic, e-mail: dosly@math.muni.cz, houska@math.muni.cz
Abstract: Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator $\ell(y)\equiv{1\over w(t)}\ddif{(r(t)\ddif{y})}$, $t\in[a,\infty)$ are established. These conditions are based on a recently proved relationship between spectral properties of $\ell$ and oscillation of a certain associated second order differential equation.
Keywords: singular differential operator, property BD, oscillation criteria, principal solution
Classification (MSC2000): 34C10
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