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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






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


Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 1, Pages 82–87 (Mi faa3179)  

Brief communications

Power Asymptotics of Spectral Functions of Boundary Value Problems for Generalized Second-Order Differential Equations with Boundary Conditions at a Singular Endpoint

I. S. Kats

Odessa National Academy of Food Technology

Abstract: Let $I=(-\infty,b)$, where $b\le +\infty$, and let $M(x)$, $x\in I$, be a nondecreasing function on $I$ such that $M(x)>0$ for $x\in I$. In the middle of the past century, it was proved that, in the case where $M(x)$ is Lebesgue integrable on the interval $(-\infty, c)$, $c\in I$, the boundary value problem $-\frac{d}{dM(x)} y^+ (x)=\lambda y(x)$, $x\in I$, $\lim_{x\to -\infty}y(x)=1$ is uniquely solvable for any complex $\lambda$ and has at least one spectral function $\tau (\lambda)$ (“$ ^+$” denotes right derivative).
A result relating the asymptotic behavior of $M(x)$ as $x \to -\infty$ to that of $\tau(\lambda)$ as $\lambda \to +\infty$ is announced. Similar results are also announced for two other boundary value problems with boundary conditions at a singular endpoint.

Keywords: string, boundary value problem, singular endpoint, spectral function

DOI: https://doi.org/10.4213/faa3179

Full text: PDF file (147 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2015, 49:1, 67–71

Bibliographic databases:

UDC: 517.91+517.43
Received: 13.07.2013

Citation: I. S. Kats, “Power Asymptotics of Spectral Functions of Boundary Value Problems for Generalized Second-Order Differential Equations with Boundary Conditions at a Singular Endpoint”, Funktsional. Anal. i Prilozhen., 49:1 (2015), 82–87; Funct. Anal. Appl., 49:1 (2015), 67–71

Citation in format AMSBIB
\Bibitem{Kat15}
\by I.~S.~Kats
\paper Power Asymptotics of Spectral Functions of Boundary Value Problems for Generalized Second-Order Differential Equations with Boundary Conditions at a Singular Endpoint
\jour Funktsional. Anal. i Prilozhen.
\yr 2015
\vol 49
\issue 1
\pages 82--87
\mathnet{http://mi.mathnet.ru/faa3179}
\crossref{https://doi.org/10.4213/faa3179}
\zmath{https://zbmath.org/?q=an:06485789}
\elib{http://elibrary.ru/item.asp?id=23421408}
\transl
\jour Funct. Anal. Appl.
\yr 2015
\vol 49
\issue 1
\pages 67--71
\crossref{https://doi.org/10.1007/s10688-015-0086-z}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000351307000009}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924975466}


Linking options:
  • http://mi.mathnet.ru/eng/faa3179
  • https://doi.org/10.4213/faa3179
  • http://mi.mathnet.ru/eng/faa/v49/i1/p82

    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
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:235
    Full text:58
    References:33
    First page:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020