Abstract :
By Karamata regular variation theory and constructing comparison functions, we show the exact
asymptotic behaviour of the unique classical solution u ∈ C2(Ω) ∩ C(Ω¯ ) near the boundary to a
singular Dirichlet problem −Δu = k(x)g(u),u>0, x ∈ Ω, u|∂Ω = 0, whereΩ is a bounded domain
with smooth boundary in RN; g ∈ C1((0,∞), (0,∞)), limt→0+
g(ξt)
g(t) = ξ−γ , for each ξ > 0, for
some γ >0; and k ∈ Cα
loc(Ω) for some α ∈ (0, 1), is nonnegative on Ω, which is also singular near
the boundary.
2005 Elsevier Inc. All rights reserved
Keywords :
Semilinear elliptic equations , Dirichlet problem , singularity , Karamata regular variation theory , Unique Solution , Existence , Exact asymptotic behaviour
