The boundary-value problem for differential-operator equations of the first order in a~locally convex space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2011), pp. 3-15.

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In this paper we describe a method that allows one to study boundary value problems for the first-order differential-operator equations in an arbitrary locally convex space.
Keywords: boundary value problem, locally convex space, differential-operator equation, operator order, operator type.
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N. A. Aksyonov. The boundary-value problem for differential-operator equations of the first order in a~locally convex space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2011), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2011_2_a0/

[1] Gorbachuk V. I., Gorbachuk M. L., Granichnye zadachi dlya differentsialno-operatornykh uravnenii, Nauk. dumka, Kiev, 1984 | MR | Zbl

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

[3] Trenogin V. A., “Kraevye zadachi dlya abstraktnykh ellipticheskikh uravnenii”, DAN SSSR, 170:5 (1966), 1026–1031 | MR

[4] Dezin A. A., Obschie voprosy teorii granichnykh zadach, Nauka, M., 1980 | MR | Zbl

[5] Dezin A. A., “Ob operatornykh uravneniyakh vtorogo poryadka”, Sib. matem. zhurn., 19:5 (1978), 1032–1042 | MR | Zbl

[6] Strakhov V. N., “O reshenii lineinykh nekorrektnykh zadach v gilbertovom prostranstve”, Differents. uravneniya, 1970, no. 8, 1490–1495 | Zbl

[7] Iosida K., Funktsionalnyi analiz, Mir, M., 1967 | MR

[8] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, In. lit., M., 1962 | MR

[9] Ivanov V. K., Melnikova I. V., Filinkov A. I., Differentsialno-operatornye uravneniya i nekorrektnye zadachi, Fizmatlit, M., 1995 | MR

[10] Gromov V. P., “Poryadok i tip lineinogo operatora i razlozhenie v ryad po sobstvennym funktsiyam”, DAN SSSR, 228:1 (1986), 27–31 | MR

[11] Gromov V.P., “Poryadok i tip operatora i tselye vektornoznachnye funktsii”, Uchen. zap. OGU, 1999, no. 1, 6–23

[12] Gromov V. P., Mishin S. N., Panyushkin S. V., Operatory konechnogo poryadka i differentsialno-operatornye uravneniya, OGU, Orel, 2009

[13] Mishin S. N., “O poryadke i tipe operatora”, Dokl. RAN, 381:3 (2001), 309–312 | MR | Zbl

[14] Mishin S. N., Operatory konechnogo poryadka v lokalno vypuklykh prostranstvakh i ikh primenenie, Diss. $\dots$ kand. fiz.-matem. nauk, Orel, 2002

[15] Le Khai Khoi, Vektornoznachnye funktsii i differentsialnye operatory beskonechnogo poryadka, RGU, Rostov-na-Donu, 1981

[16] Gromov V. P., “Operatornyi metod resheniya lineinykh uravnenii”, Uchen. zap. OGU, 2002, no. 3, 4–36 | MR

[17] Gromov V. P., “Analiticheskie resheniya differentsialno-operatornykh uravnenii v lokalno vypuklykh prostranstvakh”, Dokl. RAN, 394:3 (2004), 305–308 | MR | Zbl

[18] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, v. 1, Elementarnye funktsii, Fizmatlit, M., 2003 | MR