## Positive eigenvalues of second order boundary value problems and a theorem of M. G. Krein

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- by Steve Clark and Don Hinton
- Proc. Amer. Math. Soc.
**130**(2002), 3005-3015 - DOI: https://doi.org/10.1090/S0002-9939-02-06392-X
- Published electronically: March 15, 2002
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## Abstract:

Conditions are given which guarantee that the least real eigenvalue is positive for certain boundary value problems for the vector-matrix equation $-y^{\prime \prime }+p(x)y=\gamma w(x)y$. This leads to conditions which guarantee the stable boundedness, according to Krein, for solutions of $y^{\prime \prime }+\lambda p(x)y=0$ with certain real values of $\lambda$. As a consequence, a result first stated by Krein is proven.## References

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## Bibliographic Information

**Steve Clark**- Affiliation: Department of Mathematics, University of Missouri-Rolla, Rolla, Missouri 65409
- Email: sclark@umr.edu
**Don Hinton**- Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
- Email: hinton@math.utk.edu
- Received by editor(s): September 8, 2000
- Received by editor(s) in revised form: May 14, 2001
- Published electronically: March 15, 2002
- Communicated by: Carmen Chicone
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**130**(2002), 3005-3015 - MSC (2000): Primary 34C10, 34L15; Secondary 34B24, 34D10
- DOI: https://doi.org/10.1090/S0002-9939-02-06392-X
- MathSciNet review: 1908924