RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. Vyssh. Uchebn. Zaved. Mat.: Year: Volume: Issue: Page: Find

 Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 4, Pages 16–20 (Mi ivm9345)

On Fredholm solvability of the Dirichet problem for linear differential equations of infinite order

G. S. Balashova

National Research University (MPEI), 14 Krasnokazarmennaya str., Moscow, 111250 Russia

Abstract: 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, Sobolev spaces, solvability, subordinate terms.

Full text: PDF file (163 kB)
References: PDF file   HTML file

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:4, 13–17

Bibliographic databases:

UDC: 517.518

Citation: G. S. Balashova, “On Fredholm solvability of the Dirichet problem for linear differential equations of infinite order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 4, 16–20; Russian Math. (Iz. VUZ), 62:4 (2018), 13–17

Citation in format AMSBIB
\Bibitem{Bal18} \by G.~S.~Balashova \paper On Fredholm solvability of the Dirichet problem for linear differential equations of infinite order \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2018 \issue 4 \pages 16--20 \mathnet{http://mi.mathnet.ru/ivm9345} \transl \jour Russian Math. (Iz. VUZ) \yr 2018 \vol 62 \issue 4 \pages 13--17 \crossref{https://doi.org/10.3103/S1066369X18040023} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000429242100002} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85045108414}