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Computational Mathematics and Mathematical Physics

, Volume 58, Issue 12, pp 1937–1947 | Cite as

Existence Conditions of Negative Eigenvalues in the Regular Sturm–Liouville Boundary Value Problem and Explicit Expressions for Their Number

  • S. V. KurochkinEmail author
Article
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Abstract

For the regular Sturm–Liouville boundary value problem with general nonseparated self-adjoint boundary conditions, conditions for the existence of zero and negative eigenvalues and expressions for their number are obtained. The conditions are expresses in a closed form, and the coefficient functions of the original equation appear in these conditions indirectly through a single numerical characteristic.

Keywords:

Sturm–Liouville equation boundary value problem eigenvalue 

Notes

ACKNOWLEDGMENTS

I am grateful to N.B. Konyukhova for discussions of this paper and to the reviewer of its first version for valuable remarks that enabled me to improve the presentation.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of SciencesMoscowRussia

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