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Title: Asymptotic Behavior of Solutions of Semilinear Elliptic Equations Near an Isolated Singularity
Contributor(s): Cirstea, Florica Corina (author); Du, Yihong  (author)orcid 
Publication Date: 2007
DOI: 10.1016/j.jfa.2007.05.005
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Abstract: We consider the semilinear elliptic equation Δu=h(u) in Ω {0}, where Ω is an open subset of ℝ^N (N≥2) containing the origin and h is locally Lipschitz continuous on [0,∞), positive in (0,∞). We give a complete classification of isolated singularities of positive solutions when h varies regularly at infinity of index q ∈ (1,CN)(that is, limu→∞h(λu)/h(u)=λ^q, for every λ>0), where CN denotes either N/(N-2) if N≥3 or ∞ if N=2. Our result extends a well-known theorem of Véron for the case h(u)=u^q.
Publication Type: Journal Article
Source of Publication: Journal of Functional Analysis, 250(2), p. 317-346
Publisher: Academic Press
Place of Publication: United States of America
ISSN: 0022-1236
Field of Research (FOR): 019999 Mathematical Sciences not elsewhere classified
Socio-Economic Objective (SEO): 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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Appears in Collections:Journal Article
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