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 | References | Similar Articles | Additional Information

Abstract: Conditions are given which guarantee that the least real eigenvalue is positive for certain boundary value problems for the vector-matrix equation . This leads to conditions which guarantee the stable boundedness, according to Krein, for solutions of with certain real values of . 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

DOI:
https://doi.org/10.1090/S0002-9939-02-06392-X

Keywords:
Stable boundedness,
positive eigenvalues,
Opial inequality

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

Article copyright:
© Copyright 2002
American Mathematical Society