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

• Autoři: HILSCHER Roman
• Rok publikování: 2000
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Mathematica Slovaca
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Citace: HILSCHER, Roman. Spectral properties of general self-adjoint, even order differential operators. Mathematica Slovaca. Bratislava: Slovak Academy of Sciences, 2000, roč. 50, č. 2, s. 165-186, 21 s. ISSN 0139-9918.
• Obor: Obecná matematika
• Klíčová slova: (non)oscillatory equation; reciprocity principle; linear Hamiltonian system; property BD; principal solution

Popis

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.

Související projekty

• Diferenciální a funkcionálně-diferenciální rovnice