Geodesic
Construction of fundamental solutions to $B$-elliptic equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 70-75.

Voir la notice de l'article provenant de la source Math-Net.Ru

For two classes of elliptic type equations with the Bessel operator we construct fundamental solutions in explicit form.
Mots-clés : elliptic equation
Keywords: Bessel operator, fundamental solution, Horn confluent function. 
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R. M. Mavlyaviev. Construction of fundamental solutions to $B$-elliptic equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 70-75. http://geodesic.mathdoc.fr/item/IVM_2017_6_a7/

[1] Gellerstedt S., “Sur un problème aus limites pour l'équation $y^{2s}z_{xx}+z_{yy}=0$”, Arkiv Mat., Ast. och Fysik, 1935, no. 10, 25A

[2] Smirnov M. M., Vyrozhdayuschiesya ellipticheskie i giperbolicheskie uravneniya, Nauka, M., 1966

[3] Pulkin S. P., “Nekotorye kraevye zadachi dlya uravnenii $u_{xx}\pm\,u_{yy}+\frac{p}{x}u_{x}=0$”, Uchen. zap. Kuibyshevsk. gos. ped. in-ta im. V. V. Kuibysheva, 1958, no. 21, 3–55

[4] Evsin V. I., “Zadacha Kholmgrena dlya odnogo uravneniya s singulyarnymi koeffitsientami”, Differents. uravneniya, 9:1 (1973), 41–48 | MR | Zbl

[5] Evsin V. I., “Ob odnom analoge formuly Puassona”, Differents. uravneniya, 12:1 (1976), 41–45 | Zbl

[6] Volkodavov V. F., Nikolaev N. Ya., Nosov V. A., Tablitsy nekotorykh funktsii Rimana, integralov i ryadov, Kuibyshev, 1982

[7] Volkodavov V. F., Grebenschekov V. I., “Postroenie elementarnykh reshenii dlya trekh prostranstvennykh uravnenii”, Differents. uravneniya, Tr. pedinstitutov RSFSR, 8, 1976, 10–14

[8] Repin O. A., “O reshenii zadachi Dirikhle dlya odnogo uravneniya ellipticheskogo tipa s vyrozhdeniem vnutri oblasti”, Differents. uravneniya, Tr. pedinstitutov RSFSR, 8, 1976, 189–195

[9] Hasanov A., Rassias J. M., “Fundamental solutions of generalized bi-axially symmetric Helmholtz equation”, Complex Variables and Elliptic Equat., 52:8 (2007), 673–683 | DOI | MR | Zbl

[10] Hasanov A., Rassias J. M., “Fundamental solutions of two degenerated elliptic equations and solutions of boundary value problems in infinite area”, Int. J. Appl. Math. Statistics, 8:M07 (2007), 87–95 | MR | Zbl

[11] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, Nauka, M., 1973 | MR

[12] Kapilevich M. B., “O konflyuentnykh gipergeometricheskikh funktsiyakh Gorna”, Differents. uravneniya, 2:9 (1966), 1239–1254 | Zbl

[13] Olevskii M. N., “Reshenie zadachi Dirikhle, otnosyascheisya k uravneniyu $\Delta u+\frac{p}{x_{n}}\frac{\partial u}{\partial x_{n}}=\rho$ dlya polusfericheskoi oblasti”, DAN SSSR, 64:6 (1949), 767–770