Geodesic
A nonlocal problem for the Bitsadze--Lykov equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 28-35.

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We study a nonlocal boundary value problem for a degenerate hyperbolic equation. We prove that this problem is uniquely solvable if integral Volterra equations of the second kind are solvable with various values of parameters and a generalized fractional integro-differential operator with a hypergeometric Gaussian function in the kernel.
Keywords: boundary value problem, fractional integro-differential operator, integral Volterra equation. 
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O. A. Repin; S. K. Kumykova. A nonlocal problem for the Bitsadze--Lykov equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 28-35. http://geodesic.mathdoc.fr/item/IVM_2010_3_a4/

[1] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vyssh. shkola, M., 1995, 301 pp. | Zbl

[2] Saigo M., “A remark on integral operators involving the Gauss hypergeometric functions”, Math. Rep. Kyushu. Univ., 11:2 (1978), 135–143 | MR | Zbl

[3] Saigo M., “A certain boundary value problem for the Euler–Poisson–Darboux equation”, Math. Japon., 24:4 (1979), 337–385 | MR

[4] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987, 688 pp. | MR | Zbl

[5] Zhegalov V. I., “Kraevaya zadacha dlya uravneniya smeshannogo tipa s granichnym usloviem na obeikh kharakteristikakh i s razryvami na perekhodnoi linii”, Uchen. zap. Kazansk. un-ta, 122, no. 3, 1962, 3–16 | MR | Zbl

[6] Nakhushev A. M., Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006, 287 pp. | Zbl

[7] Kumykova S. K., “Nelokalnaya kraevaya zadacha dlya uravneniya Lykova”, Nelokalnye kraevye zadachi matem. fiziki i ikh prilozheniya, 1990, 67–69, Izd-vo In-ta matem., Kiev

[8] Orazov I. O., “Ob odnoi kraevoi zadache so smescheniem dlya obobschennogo uravneniya Trikomi”, Differents. uravneniya, 17:2 (1981), 339–344 | MR

[9] Repin O. A., “Nelokalnaya kraevaya zadacha dlya odnogo vyrozhdayuschegosya giperbolicheskogo uravneniya”, Dokl. RAN, 335:3 (1994), 295–296

[10] Kilbas A. A., Repin O. A., “Zadacha so smescheniem dlya parabolo-giperbolicheskogo uravneniya”, Differents. uravneniya, 34:6 (1998), 799–805 | MR | Zbl

[11] Repin O. A., “Nelokalnaya zadacha dlya parabolo-giperbolicheskogo uravneniya s drobnymi proizvodnymi v kraevom uslovii”, Neklassicheskie uravneniya matem. fiziki, Izd-vo In-ta matem., Novosibirsk, 2005, 252–257

[12] Trikomi F., Integralnye uravneniya, In. lit., M., 1960, 299 pp. | MR

[13] Nakhushev A. M., “Obratnye zadachi dlya vyrozhdayuschikhsya uravnenii i integralnye uravneniya Volterra tretego roda”, Differents. uravneniya, 10:1 (1974), 100–111 | Zbl