Electron. J. Diff. Eqns., Vol. 2002(2002), No. 34, pp. 1-12.

Constants in the oscillation theory of higher order Sturm-Liouville differential equations

Ondrej Dosly

Abstract:
We find the the exact value of a constant in some oscillation criteria for the higher order Sturm-Liouville differential equation
$$ (-1)^{n}(t^\alpha y^{(n)})^{(n)}=q(t)y . $$
We also study some general aspects in the oscillation theory of this equation.

Submitted October 25, 2001. Published April 4, 2002.
Math Subject Classifications: 34C10
Key Words: Sturm-Liouville differential equation, variational method, oscillation and non-oscillation criteria, conditional oscillation.

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Ondrej Dosly
Department of Mathematics
Masaryk University
Janaackovo nam. 2a, CZ-662 95 Brno.
(Czech Republic)
e-mail: dosly@math.muni.cz

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