Geodesic
General solution of a second-order partial differential equation in a Banach space with potential singular on manifolds
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2020), pp. 3-11.

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

In this work, we study the general solution of a second-order partial differential equation in a Banach space with a potential singular on the manifolds.
Keywords: fractional powers, elliptic operator, weakened solutions, generalized solutions, positive operator, Banach space. 
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T. N. Alikulov. General solution of a second-order partial differential equation in a Banach space with potential singular on manifolds. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2020), pp. 3-11. http://geodesic.mathdoc.fr/item/IVM_2020_10_a0/

[1] Ilin V. A., “Yadra drobnogo poryadka”, Matem. sb., 4:41 (1957), 459–480

[2] Alimov Sh. A., “Drobnye stepeni ellipticheskikh operatorov i izomorfizm klassov differentsiruemykh funktsii”, Differents. uravneniya, 9:8 (1972), 1609–1626 | MR

[3] Kostin V. A., Nebolsina M. N., “O korrektnoi razreshimosti kraevykh zadach dlya uravneniya vtorogo poryadka”, Dokl. RAN, 428:1 (2009), 20–22 | Zbl

[4] Khalmukhamedov A. R., “Ob otritsatelnykh stepenyakh singulyarnogo operatora Shrëdingera i skhodimost spektralnykh razlozhenii”, Matem. zametki, 59:3 (1996), 428–436 | MR | Zbl

[5] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967

[6] Krasnoselskii M. A., Zabreiko P. P., Pustylnik P. E., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR

[7] Alimov Sh., “Complex powers of the Schrödinger operator with singular potential”, Evraziisk. matem. zhurn., 2 (2007), 4–11

[8] Alimov Sh. A., Khalmukhamedov A. R., “Otsenki spektralnoi funktsii operatora Shrëdingera s potentsialom, udovletvoryayuschim usloviyu Kato”, Vestn. NUUz., 3 (2005), 46–50

[9] Mikhlin S. G., Mnogomernye singulyarnye integraly i integralnye uravneniya, Fizmatgiz, M., 1962 | MR

[10] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977