TY - JOUR

T1 - Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity

AU - Cîrstea, Florica Corina

AU - Du, Yihong

PY - 2007/9/15

Y1 - 2007/9/15

N2 - We consider the semilinear elliptic equation Δ u = h (u) in Ω {set minus} {0}, where Ω is an open subset of RN (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 (λ u) / h (u) = λq, 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) = uq.

AB - We consider the semilinear elliptic equation Δ u = h (u) in Ω {set minus} {0}, where Ω is an open subset of RN (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 (λ u) / h (u) = λq, 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) = uq.

KW - Elliptic equation

KW - Isolated singularity

KW - Regularly varying functions

UR - http://www.scopus.com/inward/record.url?scp=34547701913&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2007.05.005

DO - 10.1016/j.jfa.2007.05.005

M3 - Article

SN - 0022-1236

VL - 250

SP - 317

EP - 346

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -