Loading [MathJax]/jax/output/SVG/config.js
Ural Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ural Math. J.:
Year:
Volume:
Issue:
Page:
Find






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


Ural Mathematical Journal, 2021, Volume 7, Issue 1, Pages 26–37
DOI: https://doi.org/10.15826/umj.2021.1.003
(Mi umj135)
 

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

On the potentiality of a class of operators relative to local bilinear forms

Svetlana A. Budochkina, Ekaterina S. Dekhanova

Peoples' Friendship University of Russia, Moscow
Full-text PDF (151 kB) Citations (3)
References:
Abstract: The inverse problem of the calculus of variations (IPCV) is solved for a second-order ordinary differential equation with the use of a local bilinear form. We apply methods of analytical dynamics, nonlinear functional analysis, and modern methods for solving the IPCV. In the paper, we obtain necessary and sufficient conditions for a given operator to be potential relative to a local bilinear form, construct the corresponding functional, i.e., found a solution to the IPCV, and define the structure of the considered equation with the potential operator. As a consequence, similar results are obtained when using a nonlocal bilinear form. Theoretical results are illustrated with some examples.
Keywords: inverse problem of the calculus of variations, local bilinear form, potential operator, conditions of potentiality.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
Russian Foundation for Basic Research 19-08-00261
This paper was partially supported by the RUDN University Strategic Academic Leadership Program and by the Russian Foundation for Basic Research (project no. 19-08-00261a).
Bibliographic databases:
Document Type: Article
Language: English
Citation: Svetlana A. Budochkina, Ekaterina S. Dekhanova, “On the potentiality of a class of operators relative to local bilinear forms”, Ural Math. J., 7:1 (2021), 26–37
Citation in format AMSBIB
\Bibitem{BudDek21}
\by Svetlana~A.~Budochkina, Ekaterina~S.~Dekhanova
\paper On the potentiality of a class of operators relative to local bilinear forms
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 1
\pages 26--37
\mathnet{http://mi.mathnet.ru/umj135}
\crossref{https://doi.org/10.15826/umj.2021.1.003}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4301211}
\zmath{https://zbmath.org/?q=an:07407680}
\elib{https://elibrary.ru/item.asp?id=46381212}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85112014541}
Linking options:
  • https://www.mathnet.ru/eng/umj135
  • https://www.mathnet.ru/eng/umj/v7/i1/p26
  • This publication is cited in the following 3 articles:
    1. S. A. Budochkina, T. H. Luu, “On Variational Symmetries and Conservation Laws of a Fifth-order Partial Differential Equation”, Lobachevskii J Math, 45:6 (2024), 2466  crossref
    2. Ufa Math. J., 15:3 (2023), 118–128  mathnet  crossref
    3. S. A. Budochkina, T. H. Luu, “On Connection between Variationality of a Six-Order Ordinary Differential Equation and Hamilton–Ostrogradskii Equations”, Lobachevskii J Math, 42:15 (2021), 3594  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Ural Mathematical Journal
    Statistics & downloads:
    Abstract page:415
    Full-text PDF :326
    References:275
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025