Positive Eigenvalues of Second Order Boundary Value Problems and a Theorem of M. G. Krein
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.
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
Mathematics and Statistics
Keywords and Phrases
Opial inequality; Positive eigenvalues; Stable boundedness
International Standard Serial Number (ISSN)
Article - Conference proceedings
© 2002 American Mathematical Society, All rights reserved.
01 Oct 2002