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
Full-text PDF Free Access
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 $-y^{\prime \prime }+p(x)y=\gamma w(x)y$. 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
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
