Geodesic
Basis properties of a spectral
Sbornik. Mathematics, Tome 197 (2006) no. 10, pp. 1467-1487 Cet article a éte moissonné depuis la source Math-Net.Ru

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The following boundary-value problem is considered: \begin{gather*} y^{(4)}(x)-(q(x){y'}(x))'=\lambda y(x),\qquad 0<x<l, \\ 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. 
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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/

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