Entire Solution of a Singular Semilinear Elliptic Problem

Abstract The authors prove that the singular semilinear elliptic equation Δ u + p ( x ) u −γ =0, γ>0, p ( x )≥0, x ∈ R n , n ≥3, has a unique positive C loc 2+α ( R n ) solution that decays to zero near ∞ provided ∫ 0 ∞ t φ( t )  dt t )=max | x |= t p ( x ). Furthermore, they show that this condition on p is nearly optimal.