Geodesic
On the spectrum of some nonlocal elliptic boundary value problems
Sbornik. Mathematics, Tome 45 (1983) no. 4, pp. 543-553 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The author considers a second order elliptic equation in a cylinder $(0,d)\times G\subset\mathbf R^n$ with the following boundary conditions: the trace of the solution for $x_1=0,d$ is equal to a linear combination of traces for $x_1=d_i$ ($i=1,\dots,m$; $0), with the trace on the lateral surface of the cylinder equal to zero. It is proved that the spectrum of the operator under consideration is discrete and semibounded, and also that the operator itself is Fredholm. The results are applied to the study of the spectrum of a particular differential-difference operator. Bibliography: 13 titles. 
@article{SM_1983_45_4_a9,
     author = {A. L. Skubachevskii},
     title = {On the spectrum of some nonlocal elliptic boundary value problems},
     journal = {Sbornik. Mathematics},
     pages = {543--553},
     year = {1983},
     volume = {45},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_4_a9/}
}
TY  - JOUR
AU  - A. L. Skubachevskii
TI  - On the spectrum of some nonlocal elliptic boundary value problems
JO  - Sbornik. Mathematics
PY  - 1983
SP  - 543
EP  - 553
VL  - 45
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1983_45_4_a9/
LA  - en
ID  - SM_1983_45_4_a9
ER  - 
%0 Journal Article
%A A. L. Skubachevskii
%T On the spectrum of some nonlocal elliptic boundary value problems
%J Sbornik. Mathematics
%D 1983
%P 543-553
%V 45
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1983_45_4_a9/
%G en
%F SM_1983_45_4_a9
A. L. Skubachevskii. On the spectrum of some nonlocal elliptic boundary value problems. Sbornik. Mathematics, Tome 45 (1983) no. 4, pp. 543-553. http://geodesic.mathdoc.fr/item/SM_1983_45_4_a9/

[1] Danford N., Shvarts Dzh., Lineinye operatory, T. 2, Mir, M., 1966

[2] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

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

[4] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[5] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, LGU, L., 1950

[6] Tamarkin Ya. D., O nekotorykh obschikh zadachakh teorii obyknovennykh lineinykh differentsialnykh uravnenii, Petrograd, 1917 | Zbl

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

[8] Kamenskii A. G., “Kraevye zadachi dlya uravnenii s formalno simmetrichnymi differentsialno-raznostnymi operatorami”, Diff. uravneniya, 12:5 (1976), 815–824 | MR

[9] Kamynin L. I., “Edinstvennost reshenii kraevykh zadach dlya vyrozhdayuschegosya ellipticheskogo uravneniya vtorogo poryadka”, Diff. uravneniya, 14:1 (1978), 39–49 | MR | Zbl

[10] Kamynin L. I., Khimchenko B. N., “O strogom printsipe ekstremuma dlya slabo ellipticheski svyaznogo operatora vtorogo poryadka”, ZhVM i MF, 19:1 (1979), 129–142 | MR | Zbl

[11] Roitberg Ya. A., Sheftel Z. G., “Ob odnom klasse obschikh nelokalnykh ellipticheskikh zadach”, DAN SSSR, 192:3 (1970), 511–513 | MR | Zbl

[12] Roitberg Ya. A., Sheftel Z. G., “Formula Grina i teoremy o gomeomorfizmakh dlya nelokalnykh ellipticheskikh zadach”, DAN SSSR, 201:5 (1971), 1059–1062 | MR

[13] Skubachevskii A. L., Kraevye zadachi dlya ellipticheskikh uravnenii s otkloneniyami argumentov v starshikh chlenakh, Dis. na soiskanie uch. st. kand. fiz.-matem. nauk, MAI, M., 1980