Spectral properties of general self-adjoint, even order differential operators

• Authors: HILSCHER Roman
• Year of publication: 2000
• Type: Article in Periodical
• Magazine / Source: Mathematica Slovaca
• MU Faculty or unit: Faculty of Science
• Field: General mathematics
• Keywords: (non)oscillatory equation; reciprocity principle; linear Hamiltonian system; property BD; principal solution

Description

Necessary and sufficient condition for discreteness and boundedness below of the spectrum of the full-term singular differential operator

l(y)=1/w(t) \sum_k=0ⁿ [ p_k(t) y^(k) ]^(k) on [a,\infty),

is established. This condition is based on a recently proved generalized reciprocity principle for l and on the relationship between spectral properties of l and oscillation of a certain associated (2n-2)-order differential equation. An application to ''Euler-type'' fourth order operator is given.

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• Differential and functional - differential equations