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

Clark, Steve; Hinton, Don

doi:10.1090/S0002-9939-02-06392-X

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

Authors: Steve Clark and Don Hinton
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
Published electronically: March 15, 2002
MathSciNet review: 1908924
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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.

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