期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 161, 期 1, 页码 219-243出版社
ACADEMIC PRESS INC
DOI: 10.1006/jdeq.1999.3700
关键词
non-existence; moving spheres; Kelvin-transform; cooperative systems; maximum principles
类别
Based upon a new development of the method of moving spheres, we introduce a new and general approach for non-existence of positive solutions of cooperative semilinear elliptic systems with the Laplacian as principal part. For super-critical nonlinearities we prove non-existence on bounded star-shaped domains. For subcritical nonlinearities we obtain non-existence results on a class of unbounded domains, which includes e.g. the entire space, certain curved halfspaces and the complement of bounded star-shaped domains. As a by-product we also get a symmetry result on halfspaces. (C) 2000 Academic Press.
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