On the oscillation of eigenfunctions of a fourth-order spectral problem
type: Item
instance of: scholarly article
title: On the oscillation of eigenfunctions of a fourth-order spectral problem
zbMATH Open document ID: 1262.34099
DOI: 10.1134/S1064562412030155
author: Ziyatkhan S. Aliyev
author: E. A. Agaev
author: Nazim B. Kerimov
published in: Doklady Mathematics
publication date: 2012-11-15T00:00:00Z
review text: The authors consider the spectral problem for the fourth-order ordinary differential equation \[ l(y)(x):= (p(x)y''(x))'' - (q(x)y'(x))' + r(x)y(x\,) = \lambda \tau (x)y(x),\quad 0 < x < l, \] with boundary conditions \[ \begin{aligned} (py'')(0) - C_0 Ty(0) - C_1 y'(0) = 0, \\ y(0) + C_2 Ty(0) - C_0 y'(0) = 0, \\ (py'')(l) + D_0 Ty(l) + D_1 y'(0) = 0, \\ y(l) - D_2 Ty(0) + D_0 y'(l) = 0, \end{aligned} \] where \(\lambda \in \mathbb C\) is a spectral parameter, \( Ty \equiv (py'')' - qy',\) the functions \(p,r\) are strictly positive and continuous on \([0,l]\), the function \(p\) has an absolutely continuous derivative on \([0,l]\), and \(C_{i}, D_i \geq 0\) for \(i=0,1,2\) are real constants. This paper studies the structure of root subspaces and the number of zeros in \((0,l)\) of the eigenfunctions.
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34B09
zbMATH DE Number: 6106460
zbMATH Keywords: spectral boundary value problem
zbMATH Keywords: root subspaces
zbMATH Keywords: fourth-order differential equation
MaRDI profile type: Publication
cites work: A Pruefer transformation for the equation of a vibrating beam subject to axial forces
full work available at URL: s1064562412030155
OpenAlex ID: W2063579649
description: scientific article; zbMATH DE number 6106460