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

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Authors	HILSCHER Roman
Year of publication	2000
Type	Article in Periodical
Magazine / Source	Mathematica Slovaca
MU Faculty or unit	Faculty of Science
Citation
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.
Related projects:	Differential and functional - differential equations