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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 PDF
Proc. Amer. Math. Soc. 130 (2002), 3005-3015 Request permission

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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Additional 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