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Asymptotic Solutions to the Hartree Equation Near a Sphere. Asymptotics of Self-Consistent Potentials

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We consider the eigenvalue problem for the Hartree operator with a small nonlinearity coefficient. We find asymptotic eigenvalues and asymptotic eigenfunctions localized near a sphere. We obtain asymptotic expansions of self-consistent potentials.

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References

  1. V. P. Maslov, Complex Markov Chains and the Feynman Path Integral for Nonlinear Equations [in Russian], Nauka, Moscow (1976).

    MATH  Google Scholar 

  2. V. P. Maslov, “Equations of the self-consistent field,” J. Math. Sci. 11, 123–195 (1979).

    Article  MATH  Google Scholar 

  3. M. V. Karasev and V. P. Maslov, “Algebras with general commutation relations and their applications. II. Operator unitary-nonlinear equations,” J. Math. Sci. 15, No. 3, 273–368 (1981).

    Article  MATH  Google Scholar 

  4. M. V. Karasev and A. V. Pereskokov, “Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. I: The model with logarithmic singularity,” Izv. Math. 65, No. 5, 883–921 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  5. M. V. Karasev and A. V. Pereskokov, “Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. II: Localization in planar discs,” Izv. Math. 65, No. 6, 1127–1168 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. V. Pereskokov, “Asymptotic solutions of two-dimensional Hartree-type equations localized in the neighborhood of line segments,” Theor. Math. Phys. 131, No. 3, 775–790 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. V. Pereskokov, “Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle,” Theor. Math. Phys. 183, No. 1, 516–526 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. V. Pereskokov, “Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters,” Theor. Math. Phys. 187, No. 1, 511–524 (2016).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, 14, Krasnokazarmennaya St., Moscow, 111250, Russia

    A. V. Pereskokov

  2. National Research University “Higher School of Economics”, 20, Myasnitskaya St., Moscow, 101978, Russia

    A. V. Pereskokov

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  1. A. V. Pereskokov
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Correspondence to A. V. Pereskokov.

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Translated from Problemy Matematicheskogo Analiza 125, 2023, pp. 141-152.

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Pereskokov, A.V. Asymptotic Solutions to the Hartree Equation Near a Sphere. Asymptotics of Self-Consistent Potentials. J Math Sci 276, 154–167 (2023). https://doi.org/10.1007/s10958-023-06731-4

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  • DOI: https://doi.org/10.1007/s10958-023-06731-4

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