The Sturm–Liouville operator with rapidly growing potential and the asymptotics of its spectrum
https://doi.org/10.22405/2226-8383-2024-25-3-143-157
Abstract
In this paper, we study the asymptotic behavior of the discrete spectrum of the Sturm– Liouville operator given on R+ by the expression −𝑦′′ +𝑞(𝑥)𝑦 and the zero boundary condition 𝑦(0) cos 𝛼 + 𝑦′(0) sin 𝛼 = 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.
About the Author
Alisa Valerievna Kachkina
Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics
Russian Federation
Russian Federation
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Review
For citations:
Kachkina A.V. The Sturm–Liouville operator with rapidly growing potential and the asymptotics of its spectrum. Chebyshevskii Sbornik. 2024;25(3):143-157. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-3-143-157
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