On systems of elliptic equations involving subcritical or critical Sobolev exponents
type: Item
instance of: scholarly article
title: On systems of elliptic equations involving subcritical or critical Sobolev exponents
zbMATH Open document ID: 0958.35037
DOI: 10.1016/S0362-546X(99)00121-2
author: D. C. de Morais Filho
author: Claudianor O. Alves
author: Marco A. Souto
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-03-27T00:00:00Z
review text: Existence and non-existence results of positive solutions for a system of elliptic equations with Dirichlet boundary data in a bounded domain with smooth boundary are considered. A non-existence result is proved when \(\Omega\) is star shaped, using some type of Pohozaev identity for a system. Many comparisons with the corresponding scalar case of the problem treated by \textit{H. Brezis} and {L. Nirenberg} [Commun. Pure Appl. Math. 36, 437-477 (1983; Zbl 0541.35029)] are given.
reviewed by: Youssef Jabri
Mathematics Subject Classification ID: 35J50
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 1513294
zbMATH Keywords: elliptic systems
zbMATH Keywords: critical Sobolev exponent
zbMATH Keywords: Palais-Smale condition
zbMATH Keywords: mountain pass theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1513294