Positive solutions for the periodic scalar \(p\)-Laplacian: existence and uniqueness
type: Item
instance of: scholarly article
title: Positive solutions for the periodic scalar \(p\)-Laplacian: existence and uniqueness
zbMATH Open document ID: 1266.34036
author: Nikolaos S. Papageorgiou
author: Sophia Th. Kyritsi
published in: Taiwanese Journal of Mathematics
publication date: 2013-02-21T00:00:00Z
full work available at URL: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/2222
review text: The authors are concerned with the \(p\)-Laplacian nonlinear periodic boundary value problem (\(1<p<\infty\)) \[ \begin{aligned} -(| u'(t)|^{p-2}u'(t))'=f(t,u(t)),&\quad\text{ a.e. }\;t\in[0,b],\\ u(0)=u(b),\;u'(0)=u'(b),&\end{aligned} \] where the nonlinearity \(f\) is Carathéodory, satisfies a unilateral growth condition with respect to the second argument, and the ratio \(\frac{f(t,x)}{x^{p-1}}\) is assumed to be strictly monotone. Using variational methods, necessary and sufficient conditions are given to ensure the existence and the uniqueness of positive solutions in a Sobolev space.
reviewed by: Smail Djebali
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 6137972
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: unilateral growth
zbMATH Keywords: existence and uniqueness of positive solutions
zbMATH Keywords: weighted eigenvalues
MaRDI profile type: Publication
OpenAlex ID: W4252086737
DOI: 10.11650/TWJM/1500406738
description: scientific article; zbMATH DE number 6137972