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 oscillation of almost-periodic Sturm-Liouville operators with an arbitrary coupling constant


Authors: S. G. Halvorsen and A. B. Mingarelli
Journal: Proc. Amer. Math. Soc. 97 (1986), 269-272
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1986-0835878-3
MathSciNet review: 835878
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we characterize those (Bohr) almost periodic functions $ V$ on $ {\mathbf{R}}$ for which the Sturm-Liouville equations

$\displaystyle - y'' + \lambda V(x)y = 0,\quad x \in \mathbf{R},$

are oscillatory at $ \pm \infty $ for every real $ \lambda \ne 0$, or, equivalently, for which there exists a real $ \lambda \ne 0$ such that the equation has a positive solution on $ {\mathbf{R}}$.

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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34C10

Retrieve articles in all journals with MSC: 34C10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0835878-3
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society