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

Warning

This publication doesn't include Faculty of Economics and Administration. It includes Faculty of Science. Official publication website can be found on muni.cz.

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