Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator $l(y)\; =\; 1/w(t)\; (r(t)y\text{'}\text{'})\text{'}\text{'}$ on [a,\infty) are established. These conditions are based on a recently proved relationship between spectral properties of l and oscillation of a certain associated second order differential equation.

Last change: August 28, 2000. (c) Roman Hilscher