Geodesic
The Sturm–Liouville operator with rapidly growing potential and the asymptotics of its spectrum
Čebyševskij sbornik, Tome 25 (2024) no. 3, pp. 143-157 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study the asymptotic behavior of the discrete spectrum of the Sturm–Liouville operator given on $\mathbb{R}_{+}$ by the expression $-y''+q(x)y$ and the zero boundary condition $y(0)\cos {\alpha}+y'(0)\sin{\alpha}=0$, for rapidly growing potentials $q(x)$. The asymptotics of the eigenvalues of the operator for the classes of potentials are obtained, which characterize the rate of their growth at infinity.
Keywords: differential operator, spectrum, asymptotics. 
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     title = {The {Sturm{\textendash}Liouville} operator with rapidly growing potential and the asymptotics of its spectrum},
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A. Kachkina. The Sturm–Liouville operator with rapidly growing potential and the asymptotics of its spectrum. Čebyševskij sbornik, Tome 25 (2024) no. 3, pp. 143-157. http://geodesic.mathdoc.fr/item/CHEB_2024_25_3_a8/