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 -