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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
MathSciNet review: 835878
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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?)

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