Non-existence of positive solutions of Lane-Emden systems
type: Item
instance of: scholarly article
title: Non-existence of positive solutions of Lane-Emden systems
zbMATH Open document ID: 0868.35032
author: James Serrin
author: Henghui Zou
published in: Differential and Integral Equations
publication date: 1997-08-21T00:00:00Z
review text: Nonexistence of positive solutions of Lane-Emden systems is considered. The system is an extension of the celebrated Lane-Emden equation. The authors point out that: (1) In the case \(n=3\), if the positive constants \(p\) and \(q\) satisfy \(1/(p+1)+ 1/(q+1)>1/3\), then the Lane-Emden system does not admit any nonnegative and nontrivial solutions with algebraic growth at infinity. (2) If \(p\) and \(q\) satisfy either \(pq\leq 1\) or \(pq>1\) and \(\max\{2(p+1)/(pq-1), 2(q+1)/(pq-1)\}\geq n-2\), then the Lane-Emden system does not admit any nonnegative and nontrivial solutions. The proofs depend on asymptotic estimates at infinity. The techniques used in treating the single equation cannot be applied in the case of the system.
reviewed by: Ding Zhengzhong
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J45
zbMATH DE Number: 883497
zbMATH Keywords: weakly coupled elliptic system
zbMATH Keywords: nonexistence
zbMATH Keywords: asymptotic estimates at infinity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 883497