A Liouville type theorem for polyharmonic elliptic systems
type: Item
instance of: scholarly article
title: A Liouville type theorem for polyharmonic elliptic systems
zbMATH Open document ID: 1142.35020
author: Yajing Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-01-09T00:00:00Z
review text: The author deals with the following polyharmonic system \[ (-\Delta_x)^m u= v^q\quad\text{in }\mathbb{R}^N,\qquad (-\Delta_x)^m v= u^p\quad\text{in }\mathbb{R}^N.\tag{1} \] The author is mainly interested in the range of exponents \(p\), \(q> 0\) in (1), for which there are no positive classical solution.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J45
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 5083595
zbMATH Keywords: Liouville theorem
zbMATH Keywords: polyharmonic systems
zbMATH Keywords: moving planes method
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.03.027
OpenAlex ID: W2039740934
cites work: A characteristic property of spheres
cites work: Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
cites work: On the method of moving planes and the sliding method
cites work: Q4545173
cites work: Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
cites work: Classification of solutions of some nonlinear elliptic equations
cites work: Q4802371
cites work: Q4319815
cites work: Q4695147
cites work: Symmetry and related properties via the maximum principle
cites work: Q3923023
cites work: A priori bounds for positive solutions of nonlinear elliptic equations
cites work: Global and local behavior of positive solutions of nonlinear elliptic equations
cites work: Liouville-type theorems for polyharmonic systems in \(\mathbb R^N\)
cites work: A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
cites work: A rellich type identity and applications
cites work: Nonexistence of positive solutions of semilinear elliptic systems in \(\mathbb{R}^ N\)
cites work: A symmetry problem in potential theory
cites work: Q4350425
cites work: Non-existence of positive solutions of Lane-Emden systems
cites work: Q4219729
cites work: Classification of solutions of higher order conformally invariant equations
DOI: 10.1016/J.JMAA.2006.03.027
description: scientific article; zbMATH DE number 5083595