Mathematics of the USSR-Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mathematics of the USSR-Sbornik, 1978, Volume 34, Issue 4, Pages 411–424
DOI: https://doi.org/10.1070/SM1978v034n04ABEH001214
(Mi sm2535)
 

This article is cited in 3 scientific papers (total in 3 papers)

An expression for the solution of a differential equation in terms of iterates of differential operators

A. V. Babin
References:
Abstract: We obtain theorems on the expression of $A^{-1}$ in terms of iterates of the operator $A$, which is the reproducing operator of a $1$-parameter group of linear transformations of a Banach space, and whose spectrum does not surround $0$. These results are applied to first order differential equations with analytic coefficients and right-hand sides (symmetric first order systems on a compact manifold without boundary), and to second order elliptic equations (equations with a real principal part on a manifold without boundary, selfadjoint equations degenerate on the boundary of the domain, and the Dirichlet problem for a selfadjoint equation in a domain with an analytic boundary). We obtain formulas expressing the value of the solution at a point in terms of the derivatives of the coefficients and the right-hand side at this point.
Bibliography: 9 titles.
Received: 03.06.1977
Bibliographic databases:
UDC: 517.944
MSC: Primary 47A10, 47F05, 35J20; Secondary 47G05
Language: English
Original paper language: Russian
Citation: A. V. Babin, “An expression for the solution of a differential equation in terms of iterates of differential operators”, Math. USSR-Sb., 34:4 (1978), 411–424
Citation in format AMSBIB
\Bibitem{Bab78}
\by A.~V.~Babin
\paper An expression for the solution of a~differential equation in terms of iterates of differential operators
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 4
\pages 411--424
\mathnet{http://mi.mathnet.ru//eng/sm2535}
\crossref{https://doi.org/10.1070/SM1978v034n04ABEH001214}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=496590}
\zmath{https://zbmath.org/?q=an:0382.35049|0442.35056}
Linking options:
  • https://www.mathnet.ru/eng/sm2535
  • https://doi.org/10.1070/SM1978v034n04ABEH001214
  • https://www.mathnet.ru/eng/sm/v147/i4/p467
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024