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On the uniqueness criterion for solutions of the Sturm-Liouville equation

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Abstract

We consider the Sturm-Liouville equation \( - y'' + qy = \lambda ^2 y \) in an annular domain K from ℂ and obtain necessary and sufficient conditions on the potential q under which all solutions of the equation −y″(z) + q(z)y(z) = λ 2 y(z), z ∈ γ, where γ is a certain curve, are unique in the domain K for all values of the parameter λ ∈ ℂ.

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  1. Bashkiria State University, Ufa, Russia

    Kh. K. Ishkin

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  1. Kh. K. Ishkin
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Correspondence to Kh. K. Ishkin.

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Original Russian Text © Kh. K. Ishkin, 2008, published in Matematicheskie Zametki, 2008, Vol. 84, No. 4, pp. 552–566.

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Ishkin, K.K. On the uniqueness criterion for solutions of the Sturm-Liouville equation. Math Notes 84, 515–528 (2008). https://doi.org/10.1134/S000143460809023X

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