Integral averages and oscillation criteria for half-linear partial differential equation.
type: Item
instance of: scholarly article
title: Integral averages and oscillation criteria for half-linear partial differential equation.
zbMATH Open document ID: 1046.35034
DOI: 10.1016/S0096-3003(03)00198-X
author: Robert Mařík
published in: Applied Mathematics and Computation
publication date: 2004-03-14T00:00:00Z
review text: The aim of this paper is to extend the technique of weighted integral averages to the half-linear partial differential equation \[ \Delta_p u+ c(x)\Phi(u)= 0,\tag{E} \] where \(\Delta_p u\equiv \text{div}(\| u\|^{p-2}\nabla u)\), \(p> 1\) is the \(p\)-Laplacian, \(\Phi(u)=| u|^{p-2} u=| u|^{p-1}\text{sgn\,}u\), and \(x= (x_i)^n_{i=1}\in \mathbb{R}^n\). On the one hand, the author obtains new oscillation criteria for (E) which can remove the disadvantage of some previous theorems, and on the other hand he shows that this technique allows to obtain oscillation criteria not only for the exterior of a ball, but also for different types of unbounded domains. Some illustrative examples are given.
reviewed by: Marian Ivanovici
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 2056329
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: oscillatory solution
zbMATH Keywords: Riccati equation
zbMATH Keywords: half-linear equation
Wikidata QID: Q115339735
MaRDI profile type: Publication
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full work available at URL: s0096-3003(03)00198-x
OpenAlex ID: W2123339913
description: scientific article; zbMATH DE number 2056329