Sufficient conditions for functions to form Riesz bases in \(L_2\) and applications to nonlinear boundary-value problems
type: Item
instance of: scholarly article
zbMATH Open document ID: 1009.34077
publication date: 2002-01-24T00:00:00Z
full work available at URL: https://eudml.org/doc/122516
full work available at URL: abstr.html
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 34L30
Mathematics Subject Classification ID: 41A58
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1685995
zbMATH Keywords: Riesz basis
zbMATH Keywords: infinite sequence of solutions
zbMATH Keywords: nonlinear boundary value problem
author: P. E. Zhidkov
MaRDI profile type: Publication
title: Sufficient conditions for functions to form Riesz bases in \(L_2\) and applications to nonlinear boundary-value problems
published in: Electronic Journal of Differential Equations (EJDE)
review text: The aim of this paper is to improve a result due to \textit{P. E. Zhidkov} [Nonlinear Anal., Theory Methods and Appl. 43A, No. 4, 471-483 (2001; Zbl 0972.34016)], where the following nonlinear problem is considered NEWLINE\[NEWLINEu''= f(u^2)u,\quad u= u(x),\quad x\in (0,1),\quad u(0)= u(1)= 0,NEWLINE\]NEWLINE where \(f(u^2)u\) is continuously differentiable for \(u\in \mathbb{R}\), \(f(0)\geq 0\) and \(f(+\infty)= -\infty\). New properties of the standard system \(\{u_n\}\) in \(L_2\) are presented.
reviewed by: Pavol Chocholatý
description: scientific article; zbMATH DE number 1685995