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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
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
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
Linking options:
https://www.mathnet.ru/eng/im494https://doi.org/10.1070/IM2004v068n04ABEH000494 https://www.mathnet.ru/eng/im/v68/i4/p3
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Abstract page: | 1082 | Russian version PDF: | 298 | English version PDF: | 29 | References: | 90 | First page: | 1 |
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