Uniqueness of a positive solution to the Dirichlet problem for a quasilinear equation with \(p\)-Laplacian in a ball
type: Item
instance of: scholarly article
title: Uniqueness of a positive solution to the Dirichlet problem for a quasilinear equation with \(p\)-Laplacian in a ball
zbMATH Open document ID: 1234.35118
DOI: 10.3103/S1066369X1110001X
published in: Russian Mathematics
publication date: 2011-11-21T00:00:00Z
review text: The author proves the existence of a unique, positive, radial solution for the equation \(\Delta_p u + |x|^m |u|^q = 0 \) in the unit ball in \(\mathbb{R}^n\) with \(n\geq 2\) with zero Dirichlet boundary conditions. For \(1<p \leq 2\) (in the case \(n = 2\), \(1< p<2\)), if \(1 < q \leq \frac{(p-1)(m+n)}{n-p}\), it is shown that the problem admits a unique, positive, radial solution.
reviewed by: Florin Catrina
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35B09
zbMATH DE Number: 5975562
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: quasilinear equation with \(p\)-Laplacian
zbMATH Keywords: unique positive radial solution
author: É. I. Abduragimov
MaRDI profile type: Publication
cites work: Global and local behavior of positive solutions of nonlinear elliptic equations
cites work: On the Elliptic Equations Δu = K(x)u σ and Δu = K(x)e 2u
cites work: Positive solutions of quasilinear elliptic equations
cites work: On positive radial symmetric solution of the Dirichlet problem for a certain nonlinear equation and a numerical method for its evaluation
cites work: Uniqueness of a positive radially symmetric solution of the Dirichlet problem for certain nonlinear differential equation of the second order in a ball
description: scientific article; zbMATH DE number 5975562