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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 1, Pages 155–186 (Mi izv609)  

This article is cited in 1 scientific paper (total in 1 paper)

Approximation by step functions of functions belonging to Sobolev spaces and uniqueness of solutions of differential equations of the form $u-F(x,u,u')$

T. Yu. Semenova

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper deals with the approximation of functions belonging to the Sobolev spaces $W^1_\infty$ and $W^1_2$ by functions of the form $\varphi=\sum_{k=1}^n a_k \chi_{[x_k,x_k+d]}$. The results obtained are applied to the study of the stability of solutions of non-linear second-order differential equations of a special form. We consider the problem of whether two solutions can coincide given supplementary information in terms of the values of the functionals $l_{x_k}(u)=\frac{1}{d}\int_{x_k}^{x_k+d}u(t) dt$, $k=1,…,n$, defined on the solutions.

DOI: https://doi.org/10.4213/im609

Full text: PDF file (781 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2007, 71:1, 149–180

Bibliographic databases:

UDC: 517.9
MSC: 41A25, 41A30, 34B05
Received: 06.10.2005
Revised: 23.03.2006

Citation: T. Yu. Semenova, “Approximation by step functions of functions belonging to Sobolev spaces and uniqueness of solutions of differential equations of the form $u-F(x,u,u')$”, Izv. RAN. Ser. Mat., 71:1 (2007), 155–186; Izv. Math., 71:1 (2007), 149–180

Citation in format AMSBIB
\Bibitem{Sem07}
\by T.~Yu.~Semenova
\paper Approximation by step functions of functions belonging to Sobolev spaces
and uniqueness of solutions of~differential equations of the form $u''=F(x,u,u')$
\jour Izv. RAN. Ser. Mat.
\yr 2007
\vol 71
\issue 1
\pages 155--186
\mathnet{http://mi.mathnet.ru/izv609}
\crossref{https://doi.org/10.4213/im609}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2477277}
\zmath{https://zbmath.org/?q=an:05241938}
\elib{http://elibrary.ru/item.asp?id=9450960}
\transl
\jour Izv. Math.
\yr 2007
\vol 71
\issue 1
\pages 149--180
\crossref{https://doi.org/10.1070/IM2007v071n01ABEH002353}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000246660400007}
\elib{http://elibrary.ru/item.asp?id=13550659}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34249791188}


Linking options:
  • http://mi.mathnet.ru/eng/izv609
  • https://doi.org/10.4213/im609
  • http://mi.mathnet.ru/eng/izv/v71/i1/p155

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. Yu. Semenova, “Conditions on Determining Functionals for Subsets of Sobolev Space”, Math. Notes, 86:6 (2009), 831–841  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:348
    Full text:108
    References:48
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019