Generalized averages for solutions of nonlinear operators
type: Item
instance of: scholarly article
title: Generalized averages for solutions of nonlinear operators
zbMATH Open document ID: 0971.34010
author: Xiaojing Yang
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-10-30T00:00:00Z
review text: The author considers the twopoint boundary value problem \[ \bigl( \varphi(u') \bigr)'+f(u)=0,\;u(0)=u(T)=0, \] with \(\varphi\in C'(\mathbb{R},\mathbb{R})\), \(\varphi\) is strictly increasing, \(\varphi(\mathbb{R}) =\mathbb{R}\) and \(\varphi(0)=0\). By a suitable transformation, the equation is reduced to a simple form and known eigenvalue problem results are applied to obtain a generalized average result for positive solutions.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 1539405
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: positive solutions
zbMATH Keywords: \(p\)-Laplacian
reviewed by: Olusola Akinyele
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7077
OpenAlex ID: W1993815670
cites work: Generalized averages for solutions of two-point Dirichlet problems
cites work: A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
DOI: 10.1006/JMAA.2000.7077
description: scientific article; zbMATH DE number 1539405