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Oscillation and spectral properties of a class of singular self-adjoint differential operators. (English) Zbl 0889.34029

Oscillation and spectral properties of the one-term differential operator \[ l(y)= (-1)^n(r(t) y^{(n)})^{(n)}/w(t),\quad t\in I= [a,\infty), \] are investigated. It is shown that certain recently established necessary conditions for discreteness and boundedness from below of the spectrum of \(l\) are also sufficient for this property.
Reviewer: P.Smith (Keele)

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34L05 General spectral theory of ordinary differential operators
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