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Asymptotic integration of the Cauchy problem with countably multiple spectrum

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Literature cited

  1. S. A. Lomov, Introduction to the General Theory of Singular Perturbations [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  2. A. G. Eliseev and S. A. Iomov, “The perturbation method in a Banach space,” Dokl. Akad. Nauk SSSR,264, No. 1, 34–38 (1982).

    Google Scholar 

  3. M. P. Myagkova, “The regularized asymptotic of the Cauchy problem in the case of identically multiple spectral points,” in: All-Union Conference on Asymptotic Methods [in Russian], ILIM, Frunze (1975), pp. 327–329.

    Google Scholar 

  4. I. S. Lomov, “Regularization of singular perturbations in terms of the spectrum of the lmit operator,” Vestn. Mosk. Gos. Univ., Ser. Mekh., Mat., No. 3, 6–13 (1975).

    Google Scholar 

  5. N. I. Kabatsii, “Asymptotic solutions a mixed boundary-value problem for a parabolic equation,” in: All-Union Conference on Asymptotic Methods [in Russian], Part 1, Nauka, Alma-Ata (1979), pp. 108–109.

    Google Scholar 

  6. N. N. Prilepin, “The method of regularization for the solution of certain parabolic problems under the existence of the zero point of the spectrum,” in: All-Union Conference on Asymptotic Methods [in Russian], Part 1, Nauka, Alma-Ata (1979), pp. 106–108.

    Google Scholar 

  7. Kh. L. Territin, “Asymptotic expansions of solutions of ordinary differential equations that contain a small parameter,” Matematika,1, No. 2, 29–59 (1957).

    Google Scholar 

  8. S. F. Feshchenko, N. I. Shkil', and L. D. Nikolenko, Asymptotic Methods in the Theory of Linear Differential Equations [in Russian], Naukova Dumka, Kiev (1966).

    Google Scholar 

  9. A. G. Eliseev, “The theory of perturbations in a finite-dimensional Banach space in the case of multiple spectrum of the limit operator,” in: Methods of Small Parameter and Their Application [in Russian], Abstracts of Lectures at the All-Union School Seminar, Minsk (1982), pp. 78–100.

  10. V. A. Al'in, “Necessary and sufficient conditions for the basicity of a subsystem of the eigenfunctions and associated eigenfunctions of M. V. Keldysh's pencil of ordinary differential operators,” Dokl. Akad. Nauk SSSR,227, No. 4, 796–799 (1976).

    Google Scholar 

  11. N. I. Ionkin, “Solution of a boundary-value problem of the theory of heat conduction with a nonclassical boundary condition,” Differents. Uravn.,13, No. 2, 294–304 (1977).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 35, No. 1, pp. 63–82, January, 1984.

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Bobodzhanov, A.A., Lomov, S.A. Asymptotic integration of the Cauchy problem with countably multiple spectrum. Mathematical Notes of the Academy of Sciences of the USSR 35, 35–47 (1984). https://doi.org/10.1007/BF01142292

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