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Nonlocal Problem for the Abstract Bessel—Struve Equation

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Abstract

We find sufficient conditions for the unique solvability of nonlocal problem for the abstract Bessel—Struve differential equation. Both nonlocal conditions are written with the help of Krdelyi—Kober operators.

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References

  1. Glushak, A.V. “Abstract Cauchy Problem for the Bessel–Struve Equation”, Differ. Equ. 53 (7), 864–878 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  2. Zheng, Q. “Integrated Cosine Functions”. Internat. J. Math, and Math. Sci. 19 (3), 575–580 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang. J. Zheng, Q. “On α-times Integrated Cosine Functions”, Math. Jap. 50 (3), 401–408 (1999).

    MathSciNet  MATH  Google Scholar 

  4. Kostić, M. Generalized Semigroups and Cosine Funetians (Matematički institut SANU, Beograd, 2011).

    MATH  Google Scholar 

  5. Lebedev, N.N. Speeial Minetions and their Applieations (Fizmatgiz, Moscow, 1963) [in Russian].

    Google Scholar 

  6. Samko, S.G., Kilbas, A.A., Marieliev, O.I. Integrals and Derivatives of Fractional Order and Some their Applieations (Nauka i Tekhnika, Minsk, 1987) [in Russian].

    Google Scholar 

  7. Kamynin, V.L. “The Inverse Problem of the Simultaneous Determination of the Right-hand Side and the Lowest Coefficient in a Parabolic Equation with Many Space Variables”. Math. Notes 97 (3–4), 349–301 (2015).

    Google Scholar 

  8. Tikhonov, I.V. “On the Solvability of a Problem with a Nonlocal Integral Condition for a Differential Kquation in a Banach Space”. Differential Equations 34 (6), 841–844 (1998).

    MathSciNet  MATH  Google Scholar 

  9. Sil’chenko, Yu.T. “A Parabolic Equation with Nonlocal Conditions”, Journal of Mathematical Sciences 149 (6), 1701–1707 (2008).

    Article  MathSciNet  Google Scholar 

  10. Tikhonov, I.V. “Uniqueness Theorems for Linear Nonlocal Problems for Abstract Differential Equations”, Izv. Math. 67 (2), 333–303 (2003).

    Google Scholar 

  11. Glushak, A.V. “A Nonlocal Problem for an Abstract Euler-Poisson-Darboux Equation”. Russian Math. (Iz. VUZ) 60 (6), 21–28 (2010).

    Article  MathSciNet  Google Scholar 

  12. Glushak, A.V. “About Solvability of One Nonlocal Problem for Abstract Malmsten Equation”, Uchen. Zap. Bryansk. Cos. Univ.: Fiz.-Materm. Nauki / Biolog. Nauki / Veter. Nauki 3, 22–30 (2010).

    Google Scholar 

  13. Glushak, A.V., Pokruehin, O.A. “Criterion for the Solvability of the Cauchy Problem for an Abstract Euler Poisson Darboux Equation”, Differ. Equ. 52 (1), 39–57 (2010).

    Article  MathSciNet  Google Scholar 

  14. Prudnikov, A.P., Brychkov, Yu.A., Marichev, O.I. Integrals and Series. Speeial Functions (Nauka, Moscow, 1983) [in Russian].

    MATH  Google Scholar 

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Correspondence to A. V. Glushak.

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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 7, pp. 29–38.

Funding

The work was supported by Russian Foudation for Basic Research, grant no. 19-01-00732-a

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Glushak, A.V. Nonlocal Problem for the Abstract Bessel—Struve Equation. Russ Math. 63, 24–32 (2019). https://doi.org/10.3103/S1066369X1907003X

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  • DOI: https://doi.org/10.3103/S1066369X1907003X

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