Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



On the existence of nonsimple real eigenvalues for general Sturm-Liouville problems

Author: A. B. Mingarelli
Journal: Proc. Amer. Math. Soc. 89 (1983), 457-460
MSC: Primary 34B25
MathSciNet review: 715866
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Sturm-Liouville eigenvalue problem $ - y'' + q(t)y = \lambda r(t)y$, $ t \in [a, b]$, where $ y$ is required to satisfy a pair of homogeneous separated boundary conditions at $ t = a$, $ t = b$ is considered when no sign restrictions are imposed upon the coefficients $ q$, $ r$. It will be shown that the general eigenvalue problem above can admit at most finitely many nonsimple real eigenvalues (in some cases none at all). Moreover, we will show by means of an example that nonsimple real eigenvalues may occur in the case when each of $ q$ and $ r$ changes sign in $ (a, b)$ and under Dirichlet boundary conditions.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B25

Retrieve articles in all journals with MSC: 34B25

Additional Information

Keywords: Sturm-Liouville problems, nonsimple eigenvalues
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society