Voir la notice de l'article provenant de la source Math-Net.Ru
@article{IVM_2022_7_a5, author = {T. G. Ergashev and Z. R. Tulakova}, title = {A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain}, journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika}, pages = {58--72}, publisher = {mathdoc}, number = {7}, year = {2022}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/IVM_2022_7_a5/} }
TY - JOUR AU - T. G. Ergashev AU - Z. R. Tulakova TI - A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2022 SP - 58 EP - 72 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2022_7_a5/ LA - ru ID - IVM_2022_7_a5 ER -
%0 Journal Article %A T. G. Ergashev %A Z. R. Tulakova %T A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain %J Izvestiâ vysših učebnyh zavedenij. Matematika %D 2022 %P 58-72 %N 7 %I mathdoc %U http://geodesic.mathdoc.fr/item/IVM_2022_7_a5/ %G ru %F IVM_2022_7_a5
T. G. Ergashev; Z. R. Tulakova. A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2022), pp. 58-72. http://geodesic.mathdoc.fr/item/IVM_2022_7_a5/
[1] Ergashev T. G., Tulakova Z. R., “Zadacha Dirikhle dlya ellipticheskogo uravneniya s neskolkimi singulyarnymi koeffitsientami v beskonechnoi oblasti”, Izv. vuzov. Matem., 2021, no. 7, 81–91 | Zbl
[2] Ergashev T. G., Tulakova Z. R., Lauricella hypergeometric function and its application to the solution of the Neumann problem for a multidimensional elliptic equation with several singular coefficients in an infinite domain, 2021, arXiv: 2108.02691 | MR
[3] Smirnov M. M., Vyrozhdayuschiesya ellipticheskie i giperbolicheskie uravneniya, Nauka, M., 1966 | MR
[4] Amanov D., “Nekotorye kraevye zadachi dlya vyrozhdayuschegosya ellipticheskogo uravneniya v neogranichennoi oblasti”, Izv. AN UzSSR. Ser. Fiz. Matem., 1984, no. 1, 8–13 | MR | Zbl
[5] Amanov D., “Kraevaya zadacha dlya uravneiya ${\rm sgn}\,y |y|^mu_{xx}+x^nu_{yy}=0$ v neogranichennoi oblasti”, Izv. AN UzSSR. Ser.: Fiz. Matem., 1984, no. 2, 8–10 | MR | Zbl
[6] Flaisher N. M., “Ob odnoi zadache Franklya dlya uravneniya Lavrenteva v sluchae neogranichennoi oblasti”, Izv. vuzov. Matem., 1966, no. 6, 152–156
[7] Marichev O. I., “Singulyarnye kraevye zadachi dlya obobschennogo dvuosesimmetricheskogo uravneniya Gelmgoltsa”, DAN SSSR, 230:3 (1976), 523–526 | MR | Zbl
[8] Shimkovich E. V., “O vesovykh kraevykh zadachakh dlya vyrozhdayuschegosya ellipticheskogo uravneniya v polupolose”, Litovsk. matem. sb., 1990, no. 30, 185–196 | MR | Zbl
[9] Ruziev M. Kh., “O nelokalnoi zadache dlya uravneniya smeshannogo tipa s singulyarnym koeffitsientom v neogranichennoi oblasti”, Izv. vuzov. Matem., 2010, no. 11, 41–49
[10] Repin O. A., Lerner M. E., “O zadache Dirikhle dlya obobschennogo dvuosesimmetricheskogo uravneniya Gelmgoltsa v pervom kvadrante”, Vestn. Samarsk. gos. tekh. un-ta. Ser. fiz.-matem. nauki, 1998, no. 6, 5–8
[11] Lerner M. E., Repin O. A., “Nelokalnye kraevye zadachi v vertikalnoi polupolose dlya obobschennogo osesimmetricheskogo uravneniya Gelmgoltsa”, Differents. uravneniya, 37:11 (2001), 1562–1564 | MR | Zbl
[12] Abashkin A. A., “Ob odnoi nelokalnoi zadache dlya osesimmetricheskogo uravneniya Gelmgoltsa”, Vestn. Samarsk. gos. tekh. un.ta. Ser. fiz.-matem. nauki, 24:3 (2011), 26–34 | Zbl
[13] Abashkin A. A., “Ob odnoi zadache dlya obobschennogo dvuosesimmetricheskogo uravneniya Gelmgoltsa v beskonechnoi polupolose”, Vestn. Samarsk. gos. tekh. un-ta. Ser. fiz.-matem. nauki, 26:1 (2012), 39–45 | Zbl
[14] Abashkin A. A., “Ob odnoi vesovoi kraevoi zadache v beskonechnoi polupolose dlya dvuosesimmetricheskogo uravneniya Gelmgoltsa”, Izv. vuzov. Matem., 2013, no. 6, 3–12 | MR | Zbl
[15] Khasanov A., Gipergeometricheskie funktsii i ikh primeneniya k resheniyu kraevykh zadach dlya vyrozhdayuschikhsya differentsialnykh uravnenii vtorogo poryadka, Diss. \ldots dokt. fiz.-matem. nauk, In-t matem. i informatsionnykh tekhnologii, Tashkent, 2009
[16] Karimov K. T., “Zadacha Keldysha dlya trekhmernogo uravneniya smeshannogo tipa s tremya singulyarnymi koeffitsientami v polubeskonechnom parallelepipede”, Vestn. Udmurtsk. un-ta. Ser. Matem. Mekhan. Kompyut. nauki, 30:1 (2020), 31–48 | MR | Zbl
[17] Karimov K. T., “Nonlocal problem for an elliptic equation with singular coefficients in a semi-infinite parallelepiped”, Lobachevskii J. Math., 41:1 (2020), 46–57 | DOI | MR | Zbl
[18] Karimov K. T., “Boundary value problems in a semi-infinite Parallelepiped for an elliptic equation with three singular coefficients”, Lobachevskii J. Math., 42:3 (2021), 560–571 | DOI | MR | Zbl
[19] Salakhitdinov M. S., Khasanov A., “K teorii mnogomernogo uravneniya Gellerstedta”, Uzbeksk. matem. zhurn., 2007, no. 3, 95–109 | Zbl
[20] Srivastava H. M., Karlsson P. W., Multiple Gaussian Hypergeometric Series, John Wiley and Sons, Halsted Press, New York–Chichester–Brisbane–Toronto; Ellis Horwood Limited, Chichester, 1985 | MR | Zbl
[21] Appell P., Kampe de Feriet J., Fonctions Hypergeometriques et Hyperspheriques. Polynomes d'Hermite, Gauthier - Villars, Paris, 1926
[22] Ergashev T. G., “Generalized Holmgren problem for an elliptic equation with several singular coefficients”, Diff. Equat., 56:7 (2020), 842–856 | DOI | MR | Zbl
[23] Hasanov A., Ergashev T. G., “New decomposition formulas associated with the Lauricella multivariable hypergeometric functions”, Montes Taurus J. Pure and Apll. Math., 3:3 (2021), 317–326
[24] Ergashev T. G., “Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients”, J. Siberian Federal Univ. Math. and Phys., 13:1 (2020), 48–57 | DOI | MR | Zbl
[25] Erdelyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher Transcendental Functions., v. 1, McGraw-Hill Book Company, New York–Toronto–London, 1953 | MR
[26] Gradshteyn I. S., Ryzhik I. M., Table of Integrals, Series and Products, 7th edition, Academic Press, Elsevier, Amsterdam–Boston–Heidelberg–London–New York–Oxford–Paris–San Diego–San Francisco–Singapore–Sydney–Tokyo, 2007 | MR | Zbl