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Izvestiya: Mathematics, 2004, Volume 68, Issue 4, Pages 645–658
DOI: https://doi.org/10.1070/IM2004v068n04ABEH000494
(Mi im494)
 

This article is cited in 12 scientific papers (total in 12 papers)

On a fourth-order problem with spectral and physical parameters in the boundary condition

J. Ben Amaraa, A. A. Vladimirovb

a University of 7-th November at Carthage
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: We consider the following fourth-order boundary-value problem:
\begin{gather*} [(py'')'-qy']'=\lambda ry, \\ y(0)=y'(0)=y''(1)=[(py'')'-qy'](1)+\lambda my(1)=0 \end{gather*}
with spectral parameter $\lambda\in\mathbb C$ and physical parameter $m\in\mathbb R$. We assign to this problem a linear pencil of bounded operators $T_m=T_m(\lambda)$ depending on the physical parameter $m$ and acting from $\mathcal H_2=\{y\mid y\in W_2^2[0,1],\ y(0)=y'(0)=0\}$ to the dual space $\mathcal H_{-2}$. We study the spectral properties of $T_m$ and use the results of this study to describe properties of the eigenvalues of the problem for various values of $m$. In particular, we establish asymptotics of these eigenvalues as $m\nearrow0$.
Received: 28.10.2003
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2004, Volume 68, Issue 4, Pages 3–18
DOI: https://doi.org/10.4213/im494
Bibliographic databases:
UDC: 517.984
Language: English
Original paper language: Russian
Citation: J. Ben Amara, A. A. Vladimirov, “On a fourth-order problem with spectral and physical parameters in the boundary condition”, Izv. RAN. Ser. Mat., 68:4 (2004), 3–18; Izv. Math., 68:4 (2004), 645–658
Citation in format AMSBIB
\Bibitem{BenVla04}
\by J.~Ben Amara, A.~A.~Vladimirov
\paper On a~fourth-order problem with spectral and physical parameters in the boundary condition
\jour Izv. RAN. Ser. Mat.
\yr 2004
\vol 68
\issue 4
\pages 3--18
\mathnet{http://mi.mathnet.ru/im494}
\crossref{https://doi.org/10.4213/im494}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2084560}
\zmath{https://zbmath.org/?q=an:1090.34067}
\transl
\jour Izv. Math.
\yr 2004
\vol 68
\issue 4
\pages 645--658
\crossref{https://doi.org/10.1070/IM2004v068n04ABEH000494}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746640988}
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  • https://doi.org/10.1070/IM2004v068n04ABEH000494
  • https://www.mathnet.ru/eng/im/v68/i4/p3
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1082
    Russian version PDF:298
    English version PDF:29
    References:90
    First page:1
     
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