Abstract
The purpose of this paper is to construct positive solutions of the semilinear elliptic equation −Δu = up in ℝ+N with a singular Dirichlet boundary condition. We show that for p > (N+1)=(N−1) there exists a positive singular solution which behaves like |x|−2/(p−1) as |x| → 0 and like the Poisson kernel as |x| → ∞.
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