Differential and Integral Equations

The virial theorem for higher-order differential operators

Horst Behncke and Don Hinton

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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

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

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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