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

Halvorsen, S. G.; Mingarelli, A. B.

doi:10.1090/S0002-9939-1986-0835878-3

On the oscillation of almost-periodic Sturm-Liouville operators with an arbitrary coupling constant
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by S. G. Halvorsen and A. B. Mingarelli

Proc. Amer. Math. Soc. 97 (1986), 269-272

DOI: https://doi.org/10.1090/S0002-9939-1986-0835878-3

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

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