A Hartman-Nagumo inequality for the vector ordinary \(p\)-Laplacian and applications to nonlinear boundary value problems.
type: Item
instance of: scholarly article
title: A Hartman-Nagumo inequality for the vector ordinary \(p\)-Laplacian and applications to nonlinear boundary value problems.
zbMATH Open document ID: 1041.34011
DOI: 10.1155/S102558340200036X
author: Antonio J. Ureña
author: Jean Mawhin
published in: Journal of Inequalities and Applications
publication date: 2002-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/123663
review text: The authors prove some existence results on solutions of the system of differential equations \((\phi_{p}(x'))' = f(t,x,x'), \;0 \leq t \leq 1,\) verifying either the periodic boundary conditions \(x(0) = x(1), \;x'(0) = x'(1),\) or the Dirichlet boundary conditions \(x(0) = x_{0}, \;x(1) = x_{1}.\) Here, \(p > 1,\) \(x \in \mathbb{R}^{N}\) and \(\phi_{p}(x) = \| x \|^{p-2}x,\) if \(x \neq 0\), \(\phi_{p}(0) = 0.\) On the other hand, \(f: [0,1]\times \mathbb{R}^{N}\times \mathbb{R}^{N} \rightarrow \mathbb{R}^{N}\) is continuous and \(x_{0}, x_{1}\) are some given points of \(\mathbb{R}^{N}.\) The proofs are based on a generalization of the Hartman-Nagumo inequality to the case of the vector ordinary p-Laplacian and classical degree theory.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 1910308
zbMATH Keywords: nonlinear boundary value problems
zbMATH Keywords: ordinary p-Laplacian
zbMATH Keywords: Hartman-Nagumo inequality
zbMATH Keywords: periodic solutions
zbMATH Keywords: degree theory
reviewed by: Antonio Cañada
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1910308