Geodesic
On Fredholm solvability of the Dirichet problem for linear differential equations of infinite order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2018), pp. 16-20.

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

We propose a new approach to investigation of solvability of the Dirichlet problem for differential equations of infinite order. Namely, by using the embedding theorems for the energy spaces, obtained by the author in previous papers, the corresponding differential operator of infinite order is expressed as a sum of the main and subordinate operators of infinite order. The conditions under which the above Dirichlet problems are soluble, are established by using the main term of the corresponding differential operator.
Keywords: Dirichlet problem, equations of infinite order, solvability, subordinate terms.
Mots-clés : Sobolev spaces 
@article{IVM_2018_4_a1,
     author = {G. S. Balashova},
     title = {On {Fredholm} solvability of the {Dirichet} problem for linear differential equations of infinite order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--20},
     publisher = {mathdoc},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_4_a1/}
}
TY  - JOUR
AU  - G. S. Balashova
TI  - On Fredholm solvability of the Dirichet problem for linear differential equations of infinite order
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 16
EP  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_4_a1/
LA  - ru
ID  - IVM_2018_4_a1
ER  - 
%0 Journal Article
%A G. S. Balashova
%T On Fredholm solvability of the Dirichet problem for linear differential equations of infinite order
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 16-20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2018_4_a1/
%G ru
%F IVM_2018_4_a1
G. S. Balashova. On Fredholm solvability of the Dirichet problem for linear differential equations of infinite order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2018), pp. 16-20. http://geodesic.mathdoc.fr/item/IVM_2018_4_a1/

[1] Dubinskij Ju.A., Sobolev spaces of infinite order and differential equations, Leipzig, 1986 | MR

[2] Dubinskii Yu. A., “Prostranstva Soboleva beskonechnogo poryadka”, UMN, 46:6 (1991), 97–131 | Zbl

[3] Balashova G. S., Dubinskii Yu. A., “Ravnomernaya korrektnost semeistva nelineinykh kraevykh zadach beskonechnogo poryadka”, Differents. uravneniya, 30:4 (1994), 610–620 | Zbl

[4] Balashova G. S., “Teoremy vlozheniya dlya banakhovykh prostranstv beskonechno differentsiruemykh funktsii neskolkikh peremennykh”, Matem. zametki, 47:6 (1990), 3–14 | MR | Zbl

[5] Balashova G. S., “Ob usloviyakh prodolzheniya sleda i vlozheniya dlya banakhovykh prostranstv beskonechno differentsiruemykh funktsii”, Matem. sb., 184:1 (1993), 105–128 | MR | Zbl

[6] Mandelbroit S., Primykayuschie ryady. Regulyarizatsiya posledovatelnostei. Primeneniya, In. lit., M., 1955

[7] Vainberg M. M., Variatsionnyi metod i metod monotonnykh operatorov, Nauka, M., 1972

[8] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1976