Differential and Integral Equations

The virial theorem for higher-order differential operators

Horst Behncke and Don Hinton

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Abstract

We develop virial theorems for ordinary differential equations. Both the Finkelstein and Fock methods are used. Vanishing of boundary conditions at singular points are handled by asymptotic methods as well as conditions which guarantee that the singular point is both a strong limit point and Dirichlet. Applications are given to determine intervals which contain no eigenvalues.

Article information

Source
Differential Integral Equations, Volume 25, Number 9/10 (2012), 915-937.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012375

Mathematical Reviews number (MathSciNet)
MR2985687

Zentralblatt MATH identifier
1274.34253

Subjects
Primary: 34D10: Perturbations 34B20: Weyl theory and its generalizations 34B40: Boundary value problems on infinite intervals 34L10: Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions

Citation

Behncke, Horst; Hinton, Don. The virial theorem for higher-order differential operators. Differential Integral Equations 25 (2012), no. 9/10, 915--937. https://projecteuclid.org/euclid.die/1356012375


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