A Remark on the Existence of Entire Solutions of a Singular Semilinear Elliptic Problem

It is proved that the singular semilinear elliptic equation yDusp x.g u., 0Fp x., xgRn, 2Fn, lim sª0qg s.sq`, and ggC1 0, `., 0,`.. which is strictly decreasing in 0, `., has a unique positiveCl2oqca Rn.solution that decays to zero near ` provided H0` tw t.dt-`, where w t.smax< x