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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 6, Pages 27–35 (Mi ivm9120)  

This article is cited in 9 scientific papers (total in 9 papers)

Abstract Euler–Poisson–Darboux equation with nonlocal condition

A. V. Glushak

Belgorod State National Research University, 15 Pobedy str., Belgorod, 308015 Russia

Abstract: We find conditions for the unique solvability of nonlocal problems for abstract differential equation of the Euler–Poisson–Darboux equation. Nonlocal conditions contain either Erdelyi–Kober operator or Riemann–Liouville fractional integration operator.

Keywords: nonlocal condition, unique solvability, Euler–Poisson–Darboux equation, Erdelyi–Kober operator, Riemann–Liouville operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00197 A-2016


Full text: PDF file (186 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:6, 21–28

Bibliographic databases:

UDC: 517.983
Received: 09.10.2014

Citation: A. V. Glushak, “Abstract Euler–Poisson–Darboux equation with nonlocal condition”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 6, 27–35; Russian Math. (Iz. VUZ), 60:6 (2016), 21–28

Citation in format AMSBIB
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\by A.~V.~Glushak
\paper Abstract Euler--Poisson--Darboux equation with nonlocal condition
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 6
\pages 27--35
\mathnet{http://mi.mathnet.ru/ivm9120}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 6
\pages 21--28
\crossref{https://doi.org/10.3103/S1066369X16060037}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. L. Shishkina, S. M. Sitnik, “General form of the Euler-Poisson-Darboux equation and application of the transmutation method”, Electron. J. Differ. Equ., 2017, 177  mathscinet  zmath  isi
    2. A. V. Glushak, “Uniquely solvable problems for abstract Legendre equation”, Russian Math. (Iz. VUZ), 62:7 (2018), 1–12  mathnet  crossref  isi
    3. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426  mathnet  crossref
    4. A. Fitouhi, I. Jebabli, E. L. Shishkina, S. M. Sitnik, “Applications of the integral transforms composition method to wave-type singular differential equations and index shift transmutations”, Electron. J. Differ. Equ., 2018, 130  mathscinet  zmath  isi
    5. E. L. Shishkina, “Singular Cauchy problem for the general Euler-Poisson-Darboux equation”, Open Math., 16 (2018), 23–31  crossref  mathscinet  zmath  isi  scopus
    6. E. L. Shishkina, “Generalized Euler-Poisson-Darboux equation and singular Klein-Gordon equation”, International Conference Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 973, IOP Publishing Ltd, 2018, 012058  crossref  isi  scopus
    7. E. Shishkina, “Solution of the singular Cauchy problem for a general inhomogeneous Euler-Poisson-Darboux equation”, Carpathian J. Math., 34:2 (2018), 255–267  mathscinet  isi
    8. E. L. Shishkina, “Obschee uravnenie Eilera—Puassona—Darbu i giperbolicheskie $B$-potentsialy”, Uravneniya v chastnykh proizvodnykh, SMFN, 65, no. 2, Rossiiskii universitet druzhby narodov, M., 2019, 157–338  mathnet  crossref
    9. A. V. Glushak, “Nelokalnaya zadacha dlya abstraktnogo uravneniya Besselya–Struve”, Izv. vuzov. Matem., 2019, no. 7, 29–38  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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