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Spectral properties of fourth order differential operators. (English) Zbl 0894.34028
Summary: Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of singular differential operators \(\ell (y) \equiv \frac 1{w(t)} (r(t)y'')''\), \(t\in [a,\infty)\) 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.

MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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