Geodesic
Abstract Euler–Poisson–Darboux equation with nonlocal condition
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 27-35 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Mots-clés : nonlocal condition, Euler–Poisson–Darboux equation
Keywords: unique solvability, Erdelyi–Kober operator, Riemann–Liouville operator. 
@article{IVM_2016_6_a2,
     author = {A. V. Glushak},
     title = {Abstract {Euler{\textendash}Poisson{\textendash}Darboux} equation with nonlocal condition},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {27--35},
     year = {2016},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_6_a2/}
}
TY  - JOUR
AU  - A. V. Glushak
TI  - Abstract Euler–Poisson–Darboux equation with nonlocal condition
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2016
SP  - 27
EP  - 35
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IVM_2016_6_a2/
LA  - ru
ID  - IVM_2016_6_a2
ER  - 
%0 Journal Article
%A A. V. Glushak
%T Abstract Euler–Poisson–Darboux equation with nonlocal condition
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2016
%P 27-35
%N 6
%U http://geodesic.mathdoc.fr/item/IVM_2016_6_a2/
%G ru
%F IVM_2016_6_a2
A. V. Glushak. Abstract Euler–Poisson–Darboux equation with nonlocal condition. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 27-35. http://geodesic.mathdoc.fr/item/IVM_2016_6_a2/

[1] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhn., Minsk, 1987 | MR

[2] Tikhonov I. V., “O razreshimosti zadachi s nelokalnym integralnym usloviem dlya differentsialnogo uravneniya v banakhovom prostranstve”, Differents. uravneniya, 34:6 (1998), 841–843 | MR | Zbl

[3] Silchenko Yu. T., “Uravnenie parabolicheskogo tipa s nelokalnymi usloviyami”, SMFN, 17, 2006, 5–10 | MR

[4] Tikhonov I. V., “Teoremy edinstvennosti v lineinykh nelokalnykh zadachakh dlya abstraktnykh differentsialnykh uravnenii”, Izv. RAN. Ser. matem., 67:2 (2003), 133–166 | DOI | MR | Zbl

[5] Glushak A. V., “Operatornaya funktsiya Besselya”, Dokl. RAN, 352:5 (1997), 587–589 | MR | Zbl

[6] Vatson G. N., Teoriya besselevykh funktsii, In. lit., M., 1949

[7] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Spetsialnye funktsii, Nauka, M., 1983 | MR