Isolated Singularities of Nonlinear Elliptic Inequalities. II. Asymptotic Behavior of Solutions

We give conditions on a continuous function f: (0, ∞) → (0, ∞) which guarantee that every C2 positive solution u(x) of the differential inequalities 0 ≤ –Δu ≤ f(u) in a punctured neighborhood of the origin in ℝn (n ≥ 2) is asymptotically radial (or asymptotically harmonic) as |x| → 0+....

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Bibliographic Details
Published in:Indiana University mathematics journal 2006-01, Vol.55 (6), p.1791-1811
Main Author: Taliaferro, Steven D.
Format: Article
Language:English
Subjects:
Continuous functions
Differential equations
Elliptic equations
Exact sciences and technology
Isolated singularities
Line graphs
Mathematical analysis
Mathematical functions
Mathematical inequalities
Mathematics
Neighborhood conditions
Partial differential equations
Sciences and techniques of general use
Superharmonics
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Summary:We give conditions on a continuous function f: (0, ∞) → (0, ∞) which guarantee that every C2 positive solution u(x) of the differential inequalities 0 ≤ –Δu ≤ f(u) in a punctured neighborhood of the origin in ℝn (n ≥ 2) is asymptotically radial (or asymptotically harmonic) as |x| → 0+.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2006.55.2848