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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
References:
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
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”, Sb. Math., 202:3 (2011), 307–340
Citation in format AMSBIB
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\by L.~A.~Beklaryan
\paper The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions
\jour Sb. Math.
\yr 2011
\vol 202
\issue 3
\pages 307--340
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  • 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
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