Multiple eigenvalues of a one-dimensional quasilinear problem
type: Item
instance of: scholarly article
title: Multiple eigenvalues of a one-dimensional quasilinear problem
zbMATH Open document ID: 1245.34019
DOI: 10.1134/S106456241103015X
author: D. P. Kostomarov
author: E. A. Sheina
published in: Doklady Mathematics
publication date: 2012-01-17T00:00:00Z
review text: The authors define and analyze eigenvalue problems of second-order quasilinear differential equations in the one-dimensional formulation. A quadrature expression is derived for the inverse \(x(u)\) of the eigenfunctions \(u(x)\). A technique is developed for the study of the spectrum, which depends on the form of the nonlinearity \(f(u)\). Special attention is given to functions \(f(u)\) generating problems with multiple eigenvalues and several positive eigenfunctions. Seven versions of problems are analyzed. Future research should extend results to multidimensional formulations.
reviewed by: Shlomo Carmi
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34L10
zbMATH DE Number: 5998401
zbMATH Keywords: quasilinear differential equations
zbMATH Keywords: eigenvalues and eigenfunctions
zbMATH Keywords: torroidal plasma
zbMATH Keywords: external magnetica field
MaRDI profile type: Publication
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full work available at URL: s106456241103015x
OpenAlex ID: W2042075908
description: scientific article; zbMATH DE number 5998401