On the basis property of the system of eigenfunctions of a spectral problem with spectral parameter in the boundary condition
type: Item
instance of: scholarly article
title: On the basis property of the system of eigenfunctions of a spectral problem with spectral parameter in the boundary condition
zbMATH Open document ID: 1189.34161
DOI: 10.1134/S0012266107070038
published in: Differential Equations
publication date: 2009-11-06T00:00:00Z
review text: Consider the boundary-value problem \[ y^{(4)}(x)-(q(x)y^{\prime }(x))^{\prime }=\lambda y(x), \] \[ 0<x<l,\;y^{\prime }(0)\cos \alpha -y^{\prime \prime }(0)\sin \alpha =0,\quad y(0)\cos \beta +Ty(0)\sin \beta =0, \] \[ y^{\prime }(l)\cos \gamma +y^{\prime \prime }(l)\sin \gamma =0,\quad(a\lambda +b)y(l)-(c\lambda +d)Ty(l)=0, \] where \(\lambda \) is a spectral parameter; \(Ty:=y^{\prime \prime \prime }-qy^{\prime }\); \(q\) is a positive absolutely continuous function on the interval \([0,l]\); \(\alpha ,\beta ,\gamma ,a,b,c,\) and \(d\) are real constants; and \(0\leq \alpha ,\beta ,\gamma \leq \pi /2\), \(bc-ad>0\). The present paper studies the basis properties of the system of eigenfunctions of the boundary-value problem in the spaces \(L_{p}(0,l)\) (\(1<p<\infty \)).
reviewed by: Bilender P. Allahverdiev
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 5626741
zbMATH Keywords: boundary-value problem
zbMATH Keywords: spectral parameter in the boundary condition
zbMATH Keywords: basis property of the system of eigenfunctions
author: Nazim B. Kerimov
author: Ziyatkhan S. Aliyev
MaRDI profile type: Publication
cites work: Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
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cites work: Q3787532
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cites work: A Pruefer transformation for the equation of a vibrating beam subject to axial forces
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full work available at URL: s0012266107070038
OpenAlex ID: W1985649092
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description: scientific article; zbMATH DE number 5626741