Geodesic
A nonlocal problem for a~mixed-type equation with a~singular coefficient in an unbounded domain
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2010), pp. 41-49.

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In this paper we study a nonlocal problem for a mixed-type equation in a domain whose elliptic part is the first quadrant of the plane and the hyperbolic part is the characteristic triangle. With the help of the method of integral equations and the principle of extremum we prove the unique solvability of the considered problem.
Keywords: principle of extremum, unique solvability
Mots-clés : existence of a solution, singular coefficient. 
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M. Kh. Ruziev. A nonlocal problem for a~mixed-type equation with a~singular coefficient in an unbounded domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2010), pp. 41-49. http://geodesic.mathdoc.fr/item/IVM_2010_11_a3/

[1] Sevostyanov G. D., “Kraevaya zadacha Trikomi dlya polupolosy i chetverti ploskosti”, Volzhsk. matem. sb., 3, 1965, 312–320

[2] Gellerstedt S., “Quelques problèmes mixtes pour l`équation $y^mz_{xx}+z_{yy}=0$”, Ark. Mat. Astron. Fysik. A, 26:3 (1938), 1–32

[3] Bitsadze A. V., “Ob odnoi zadache Franklya”, DAN SSSR, 109:6 (1956), 1091–1094 | MR | Zbl

[4] Devingtal Yu. V., “O suschestvovanii i edinstvennosti resheniya odnoi zadachi F. I. Franklya”, Izv. vuzov. Matematika, 1958, no. 2, 39–51 | MR | Zbl

[5] Flaisher N. M., “Ob odnoi zadache Franklya dlya uravneniya Lavrenteva v sluchae neogranichennoi oblasti”, Izv. vuzov. Matematika, 1966, no. 6, 152–156 | MR

[6] Khairullin R. S., “Zadacha Trikomi dlya odnogo uravneniya s singulyarnymi koeffitsientami”, Izv. vuzov. Matematika, 1996, no. 3, 68–76 | MR | Zbl

[7] Polosin A. A., “Ob odnoznachnoi razreshimosti zadachi Trikomi dlya odnoi spetsialnoi oblasti”, Differents. uravneniya, 32:3 (1996), 394–401 | MR | Zbl

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

[9] Mirsaburov M., “Kraevaya zadacha dlya odnogo klassa uravnenii smeshannogo tipa s usloviem Bitsadze–Samarskogo na parallelnykh kharakteristikakh”, Differents. uravneniya, 37:9 (2001), 1281–1284 | MR | Zbl

[10] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shkola, M., 1985 | MR | Zbl

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

[12] Salakhitdinov M. S., Mirsaburov M., Nelokalnye zadachi dlya uravnenii smeshannogo tipa s singulyarnymi koeffitsientami, Izd-vo NUUz, Tashkent, 2005 | Zbl

[13] Ruziev M. Kh., “Kraevaya zadacha Trikomi dlya uravneniya smeshannogo tipa s singulyarnym koeffitsientom v neogranichennoi oblasti”, Doklady AN RUz, 2007, no. 6, 5–8

[14] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971

[15] Gakhov F. D., Cherskii Yu. I., Uravneniya tipa svertki, Nauka, M., 1978 | MR | Zbl