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MATHEMATICA BOHEMICA, Vol. 122, No. 2, pp. 153-168 (1997)
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#
Spectral properties of fourth order differential operators

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Ondrej Dosly, Roman Hilscher

* 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

**Full text of the article:**

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