Sbornik: Mathematics
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

Sbornik: Mathematics, 2011, Volume 202, Issue 3, Pages 307–340
DOI: https://doi.org/10.1070/SM2011v202n03ABEH004147 (Mi sm7534) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions

L. A. Beklaryan

Central Economics and Mathematics Institute, RAS
English version PDF (476 kB) Citations (2)
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM2011v202n03ABEH004147
Abstract: A boundary value problem and an initial-boundary value problems are considered for a linear functional differential equation of point type. A suitable scale of functional spaces is introduced and existence theorems for solutions are stated in terms of this scale, in a form analogous to Noether's theorem. A key fact is established for the initial boundary value problem: the space of classical solutions of the adjoint equation must be extended to include impulsive solutions. A test for the pointwise completeness of solutions is obtained. The results presented are based on a formalism developed by the author for this type of equation.
Bibliography: 7 titles.
Keywords: functional differential equations, scale of function spaces, impulsive solutions, analogue of Noether's theorem, pointwise completeness of solutions.
Received: 04.02.2009 and 20.10.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 3, Pages 3–36
DOI: https://doi.org/10.4213/sm7534
Bibliographic databases:
Document Type: Article
UDC: 517.911
MSC: 34K06, 34K10
Language: English
Original paper language: Russian
Citation: L. A. Beklaryan, “The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions”, Mat. Sb., 202:3 (2011), 3–36; Sb. Math., 202:3 (2011), 307–340
Citation in format AMSBIB
\Bibitem{Bek11}
\by L.~A.~Beklaryan
\paper The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions
\jour Mat. Sb.
\yr 2011
\vol 202
\issue 3
\pages 3--36
\mathnet{http://mi.mathnet.ru/sm7534}
\crossref{https://doi.org/10.4213/sm7534}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2816023}
\zmath{https://zbmath.org/?q=an:1228.34097}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2011SbMat.202..307B}
\elib{https://elibrary.ru/item.asp?id=19066263}
\transl
\jour Sb. Math.
\yr 2011
\vol 202
\issue 3
\pages 307--340
\crossref{https://doi.org/10.1070/SM2011v202n03ABEH004147}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000290671200001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959815654}
Linking options:
  • https://www.mathnet.ru/eng/sm7534
  • https://doi.org/10.1070/SM2011v202n03ABEH004147
  • https://www.mathnet.ru/eng/sm/v202/i3/p3
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:653
    Russian version PDF:190
    English version PDF:12
    References:59
    First page:19
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024