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Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters

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Abstract

We consider an eigenvalue problem for the two-dimensional Hartree operator with a small parameter at the nonlinearity. We obtain the asymptotic eigenvalues and the asymptotic eigenfunctions near the upper boundaries of the spectral clusters formed near the energy levels of the unperturbed operator and construct an asymptotic expansion around the circle where the solution is localized.

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Correspondence to A. V. Pereskokov.

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This research was performed in the framework of the governmental target program of the Russian Federation Ministry of Education and Science (Contract No. 1.756.2014/K).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 187, No. 1, pp. 74–87, April, 2016.

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Pereskokov, A.V. Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters. Theor Math Phys 187, 511–524 (2016). https://doi.org/10.1134/S0040577916040061

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  • DOI: https://doi.org/10.1134/S0040577916040061

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