Positive Eigenvalues of Second Order Boundary Value Problems and a Theorem of M. G. Krein

Author

Stephen L. Clark, Missouri University of Science and TechnologyFollow
Don B. Hinton

Abstract

Conditions are given which guarantee that the least real eigenvalue is positive for certain boundary value problems for the vector-matrix equation -y″ + p(x)y = γw(x)y. This leads to conditions which guarantee the stable boundedness, according to Krein, for solutions of y″ + λp(x)y = 0 with certain real values of λ. As a consequence, a result first stated by Krein is proven.

Recommended Citation

S. L. Clark and D. B. Hinton, "Positive Eigenvalues of Second Order Boundary Value Problems and a Theorem of M. G. Krein," Proceedings of the American Mathematical Society, vol. 130, no. 10, pp. 3005 - 3015, American Mathematical Society, Oct 2002.

The definitive version is available at https://doi.org/10.1090/S0002-9939-02-06392-X

Department(s)

Mathematics and Statistics

Keywords and Phrases

Opial inequality; Positive eigenvalues; Stable boundedness

International Standard Serial Number (ISSN)

0002-9939; 1088-6826

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2002 American Mathematical Society, All rights reserved.

Publication Date

01 Oct 2002