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singular differential operators; property BD; oscillation criteria; principal solution
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.
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