Nonexistence of radial entire solutions of elliptic systems.
type: Item
instance of: scholarly article
title: Nonexistence of radial entire solutions of elliptic systems.
zbMATH Open document ID: 1045.34003
DOI: 10.1016/S0022-0396(02)00090-6
author: Roberta Filippucci
published in: Journal of Differential Equations
publication date: 2003-04-28T00:00:00Z
review text: The author considers the quasi-variational ordinary differential system \[ [\nabla G(u,u')]'- \nabla_u G(u,u')+ Q(t, u,u')= f(t,u) \] on \(J= (T,\infty)\), \(T\geq 0\), where \(\nabla= \nabla_u\) denotes the gradient operator with respect to the second variable of the function \(G\). Also, he applies the above result to the study of nonexistence of radial solutions of elliptic systems of the general form \[ \text{div}(g(u) A(| D_u|) D_u)- \nabla_u g(u){\mathcal A}(| D_u|)= f(| x|,u),\quad x\in\mathbb{R}^n, \] which is an extension of the results of Naito-Usami, where \(D_u\) denotes the Jacobian matrix and \({\mathcal A}(s)= \int^s_0 \sigma A(\sigma)\,d\sigma\). The results are very nice.
reviewed by: J. K. Kim
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 35J45
zbMATH DE Number: 1902853
zbMATH Keywords: quasi-variational ordinary differential system
zbMATH Keywords: elliptic system
zbMATH Keywords: nonexistence
zbMATH Keywords: radial solution
MaRDI profile type: Publication
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full work available at URL: s0022-0396(02)00090-6
OpenAlex ID: W1992836836
description: scientific article; zbMATH DE number 1902853