Geodesic
On the Uniqueness Criterion for Solutions of the Sturm--Liouville Equation
Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 552-566

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We consider the Sturm–Liouville equation $$ -y''+qy=\lambda^2y $$ in an annular domain $K$ from $\mathbb C$ and obtain necessary and sufficient conditions on the potential $q$ under which all solutions of the equation $-y''(z)+q(z)y(z)=\lambda^2y(z)$, $z\in\gamma$, where $\gamma$ is a certain curve, are unique in the domain $K$ for all values of the parameter $\lambda\in\mathbb C$.
Keywords: spectral problem, holomorphic function, uniqueness problem, Bessel function, Rouché theorem, meromorphic function
Mots-clés : Sturm–Liouville equation, simple pole. 
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     author = {Kh. K. Ishkin},
     title = {On the {Uniqueness} {Criterion} for {Solutions} of the {Sturm--Liouville} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {552--566},
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     volume = {84},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a6/}
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Kh. K. Ishkin. On the Uniqueness Criterion for Solutions of the Sturm--Liouville Equation. Matematičeskie zametki, Tome 84 (2008) no. 4, pp. 552-566. http://geodesic.mathdoc.fr/item/MZM_2008_84_4_a6/