Basis properties of a spectral
Sbornik. Mathematics, Tome 197 (2006) no. 10, pp. 1467-1487
Voir la notice de l'article provenant de la source Math-Net.Ru
The following boundary-value problem is considered:
\begin{gather*}
y^{(4)}(x)-(q(x){y'}(x))'=\lambda y(x),\qquad 0,
\\
y(0)=y'(0)=y''(l)=0, \qquad
(a\lambda+b)y(l)=(c\lambda+d)Ty(l),
\end{gather*}
where $\lambda$ is the spectral parameter;
$Ty\equiv y'''-qy'$; $q(x)$ is a strictly positive absolutely
continuous function on $[0,l]$; $a$, $b$, $c$, and $d$ are
real constants such that
$bc-ad>0$. The oscillation properties of eigenfunctions are
studied and asymptotic formulae for eigenvalues and
eigenfunctions are deduced. The basis properties in $L_p(0,l)$, $1$, of the
system of eigenfunctions are investigated.
Bibliography: 20 titles.
@article{SM_2006_197_10_a4,
author = {N. B. Kerimov and Z. S. Aliyev},
title = {Basis properties of a spectral},
journal = {Sbornik. Mathematics},
pages = {1467--1487},
publisher = {mathdoc},
volume = {197},
number = {10},
year = {2006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2006_197_10_a4/}
}
N. B. Kerimov; Z. S. Aliyev. Basis properties of a spectral. Sbornik. Mathematics, Tome 197 (2006) no. 10, pp. 1467-1487. http://geodesic.mathdoc.fr/item/SM_2006_197_10_a4/