Asymptotic Behavior of Solutions of Semilinear Elliptic Equations Near an Isolated Singularity

2007

Cirstea, Florica Corina

Du, Yihong

Journal Article

en

Publication

Elsevier Inc

United States of America

10.1016/j.jfa.2007.05.005

une:4048

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.

link

Journal of Functional Analysis, 250(2), p. 317-346

1096-0783

0022-1236

317

346