Contemporary Mathematics. Fundamental Directions
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Publishing Ethics

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


CMFD:
Year:
Volume:
Issue:
Page:
Find




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

Contemporary Mathematics. Fundamental Directions, 2007, Volume 21, Pages 5–36 (Mi cmfd75)  
This article is cited in 15 scientific papers (total in 15 papers)

On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics

E. M. Varfolomeev

Peoples Friendship University of Russia
Full-text PDF (437 kB) Citations (15)
References:
PDF
HTML
Abstract: Quasilinear parabolic functional differential equations containing multiple transformations of spatial variables are considered with the Neumann boundary-value conditions. Sufficient conditions of the Andronov–Hopf bifurcation of periodic solutions are obtained along with expansions of the solutions in powers of small parameter. Spectral properties of the linearized elliptic operator of this problem are investigated. Necessary and sufficient conditions of normality are obtained for such operators. Examples on their properties are given.
English version:
Journal of Mathematical Sciences, 2008, Volume 153, Issue 5, Pages 649–682
DOI: https://doi.org/10.1007/s10958-008-9141-0
Bibliographic databases:
UDC: 517.956.4
Language: Russian
Citation: E. M. Varfolomeev, “On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics”, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), CMFD, 21, PFUR, M., 2007, 5–36; Journal of Mathematical Sciences, 153:5 (2008), 649–682
Citation in format AMSBIB
\Bibitem{Var07}
\by E.~M.~Varfolomeev
\paper On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics
\inbook Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A.~L.~Skubachevskii (Peoples' Friendship University of Russia)
\serial CMFD
\yr 2007
\vol 21
\pages 5--36
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd75}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336489}
\zmath{https://zbmath.org/?q=an:1157.35116}
\elib{https://elibrary.ru/item.asp?id=13597192}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 153
\issue 5
\pages 649--682
\crossref{https://doi.org/10.1007/s10958-008-9141-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-54249154548}
Linking options:
  • https://www.mathnet.ru/eng/cmfd75
  • https://www.mathnet.ru/eng/cmfd/v21/p5
    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Современная математика. Фундаментальные направления
    Statistics & downloads:
    Abstract page:565
    Full-text PDF :144
    References:73
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024