On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 248-263.

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

Nonlocal elliptic problems in plane domains are considered. Necessary conditions for the Fredholm solvability of such problems in weighted spaces are obtained.
@article{TM_2008_260_a16,
     author = {A. L. Skubachevskii},
     title = {On {Necessary} {Conditions} for the {Fredholm} {Solvability} of {Nonlocal} {Elliptic} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {248--263},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_260_a16/}
}
TY  - JOUR
AU  - A. L. Skubachevskii
TI  - On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2008
SP  - 248
EP  - 263
VL  - 260
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2008_260_a16/
LA  - ru
ID  - TM_2008_260_a16
ER  - 
%0 Journal Article
%A A. L. Skubachevskii
%T On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2008
%P 248-263
%V 260
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2008_260_a16/
%G ru
%F TM_2008_260_a16
A. L. Skubachevskii. On Necessary Conditions for the Fredholm Solvability of Nonlocal Elliptic Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 248-263. http://geodesic.mathdoc.fr/item/TM_2008_260_a16/

[1] Bitsadze A. V., Samarskii A. A., “O nekotorykh prosteishikh obobscheniyakh lineinykh ellipticheskikh kraevykh zadach”, DAN SSSR, 185:4 (1969), 739–740 | Zbl

[2] Skubachevskii A. L., “Nelokalnye ellipticheskie zadachi s parametrom”, Mat. sb., 121:2 (1983), 201–210 | MR

[3] Skubachevskii A. L., “Ellipticheskie zadachi s nelokalnymi usloviyami vblizi granitsy”, Mat. sb., 129:2 (1986), 279–302 | MR

[4] Skubachevskii A. L., “Razreshimost ellipticheskikh zadach s nelokalnymi usloviyami”, DAN SSSR, 291:3 (1986), 551–555 | MR

[5] Skubachevskii A. L., “O metode srezayuschikh funktsii v teorii nelokalnykh zadach”, Dif. uravneniya, 27:1 (1991), 128–139 | MR

[6] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi i uglovymi tochkami”, Tr. Mosk. mat. o-va, 16 (1967), 209–292

[7] Kishkis K. Yu., “Ob indekse zadachi A. V. Bitsadze, A. A. Samarskogo dlya garmonicheskikh funktsii”, Dif. uravneniya, 24:1 (1988), 105–110 | MR | Zbl

[8] Soldatov A. P., “Zadacha Bitsadze–Samarskogo dlya funktsii, analiticheskikh po Duglisu”, Dif. uravneniya, 41:3 (2005), 396–407 | MR | Zbl

[9] Guschin A. K., Mikhailov V. P., “O razreshimosti nelokalnykh zadach dlya ellipticheskogo uravneniya vtorogo poryadka”, Mat. sb., 185:1 (1994), 121–160 | Zbl

[10] Galakhov E. I., Skubachevskii A. L., “O szhimayuschikh neotritsatelnykh polugruppakh s nelokalnymi usloviyami”, Mat. sb., 189:1 (1998), 45–78 | MR | Zbl

[11] Skubachevskii A. L., “O sobstvennykh znacheniyakh i sobstvennykh funktsiyakh nekotorykh nelokalnykh kraevykh zadach”, Dif. uravneniya, 25:1 (1989), 127–136 | MR

[12] Gurevich P. L., “Solvability of nonlocal elliptic problems in Sobolev spaces. I, II”, Russ. J. Math. Phys., 10:4 (2003), 436–466 ; 11:1 (2004), 1–44 | MR | Zbl | MR | Zbl

[13] Gurevich P. L., “Obobschennye resheniya nelokalnykh ellipticheskikh zadach”, Mat. zametki, 77:5 (2005), 665–682 | MR | Zbl

[14] Mitidieri E., Pokhozhaev S. I., “Teoremy tipa Liuvillya dlya nekotorykh nelineinykh nelokalnykh zadach”, DAN, 399:6 (2004), 732–736 | MR

[15] Skubachevskii A. L., “On the stability of index of nonlocal elliptic problems”, J. Math. Anal. and Appl., 160:2 (1991), 323–341 | DOI | MR | Zbl

[16] Krein S. G., Lineinye uravneniya v banakhovom prostranstve, Nauka, M., 1971 | MR

[17] Skubachevskii A. L., “Nelokalnye kraevye zadachi dlya ellipticheskikh sistem v uglakh”, Tr. sem. im. I. G. Petrovskogo, 22 (2002), 283–298