Spectral properties of general self-adjoint, even order differential operators
|Year of publication||2000|
|Type||Article in Periodical|
|Magazine / Source||Mathematica Slovaca|
|MU Faculty or unit|
|Keywords||(non)oscillatory equation; reciprocity principle; linear Hamiltonian system; property BD; principal solution|
Necessary and sufficient condition for discreteness and boundedness below of the spectrum of the full-term singular differential operator
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.