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Regularity of a Problem of 3n-th Order with Decaying Boundary-Value Conditions

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Abstract

Let us consider on interval (0, 1) a differential pencil with three n-fold characteristic roots and decaying boundary-value conditions, only one of which is related to the end of 1. We solve problem of expanding of 3n times continuously differentiable function into a Fourier series in the root elements of the pencil. The studied problem essentially generalizes the previous considerations, which concern only the relatively simple cases of pencils with two n-fold characteristic roots. New method are used in estimating the resolvent of the problem. As for the problem under consideration with three n-fold characteristics, it dose not fit into the solution scheme of previous works and is associated with overcoming of exact constructions and calculations.

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References

  1. Pechentsov, A.S. “Boundary value problems for differential equations, which contain a parameter, with multiple roots of the characteristic equation”, Differentsialnye Uravneniya 20(2), 263–273 (1984) [in Russian].

    MathSciNet  Google Scholar 

  2. Omarov, M.Sh. Boundary-value problems for ordinary differential equations of fourth order with multiply characteristics (Diss. … cand. phys.-matem. nauk 66 pp., Makhachkala (1997)).

  3. Vagabov, A.I. “n-fold Fourier series expansion in root functions of a differential pencil with n-fold multiple characteristic”, Differential Equations 52(5), 531–537 (2016).

    Article  MathSciNet  Google Scholar 

  4. Vagabov, A.I. “Basis property of root functions of differential pencil of 2n-th order with n-fold characteristics”, Matem. phys. i comp. model. 21(1), 5–10 (2018) [in Russian].

    Google Scholar 

  5. Vagabov, A.I. “Equiconvergence of expansions into the trigonometric Fourier series and with respect to main functions of ordinary differential operators”, Izv. AN USSR. Ser. Matem. 48(3), 614–630 (1984) [in Russian].

    MathSciNet  MATH  Google Scholar 

  6. Naimark, M.A. Linear differential operators (Nauka, Moscow, 1969) [in Russian].

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dagestan State University, 43a M. Gadzhieva str., Makhachkala, 367025, Russia

    A. I. Vagabov

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  1. A. I. Vagabov
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Correspondence to A. I. Vagabov.

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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 11, pp. 10–15.

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Vagabov, A.I. Regularity of a Problem of 3n-th Order with Decaying Boundary-Value Conditions. Russ Math. 63, 7–12 (2019). https://doi.org/10.3103/S1066369X19110021

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  • DOI: https://doi.org/10.3103/S1066369X19110021

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