Geodesic
A nonlocal problem for a generalized Trikomi equation with a spectral parameter in the unbounded domain
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 35 (2021) no. 2, pp. 17-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article, we study a nonlocal problem for the generalized Tricomi equation with a spectral parameter in an unbounded domain, the elliptic part of which is the upper half-plane. The uniqueness of the solution to the problem posed is proved by the method of energy integrals. The existence of a solution to the problem is proved by the method of Green's functions and integral equations.
Keywords: non-local problem, unbounded domain, generalized Tricomi equation with spectral parameter, energy integrals method, Green's function method, integral equations method. 
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     author = {R. T. Zunnunov},
     title = {A nonlocal problem for a generalized {Trikomi} equation with a spectral parameter in the unbounded domain},
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R. T. Zunnunov. A nonlocal problem for a generalized Trikomi equation with a spectral parameter in the unbounded domain. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 35 (2021) no. 2, pp. 17-26. http://geodesic.mathdoc.fr/item/VKAM_2021_35_2_a1/

[1] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnyye drobnogo poryadka i nekotoryye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987, 688 pp.

[2] Salakhitdinov M. S., Urinov A. K., Krayevyye zadachi dlya uravneniya smeshannogo tipa so spektral'nym parametrom, Nauka, Tashkent, 1997, 165 pp. | MR

[3] Nakhushev A. M., “O nekotorykh zadachakh dlya giperbolicheskikh uravneniy i uravneniy smeshannogo tipa”, Differentsial'nyye uravneniya, 5:1 (1969), 44-59 | MR | Zbl

[4] Denisova Z. G., “Ob odnoy krayevoy zadache so smeshcheniyem dlya uravneniya v neogranichennoy oblasti”, Differentsial'nyye uravneniya, 14:1 (1978), 170-173 | MR | Zbl

[5] Repin O. A, Kumykova S. K., “Ob odnoy krayevoy zadache so smeshcheniyem dlya uravneniya smeshannogo tipa v neogranichennoy oblasti”, Differentsial'nyye uravneniya, 48:8 (2012), 1140-1149 | Zbl

[6] Bakiyevich N. I., “Singulyarnyye zadachi Trikomi dlya uravneniya $y^mu_{xx}+u_{yy}-\lambda^2y^m u=0$”, Izvestiya vysshikh uchebnykh zavedeniy, 1964, no. 2(39), 7-13 | MR | Zbl

[7] Muskhelishvili N. I., Singulyarnyye integral'nyye uravneniya, GIFML, M., 1962, 600 pp.