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
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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.

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