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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.

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

Bibliographic databases:

UDC: 517.518
Received: 27.01.2017

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
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\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}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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