ISOLATED SINGULARITIES OF POSITIVE SOLUTIONS OF ELLIPTIC EQUATIONS WITH WEIGHTED GRADIENT TERM

Let Omega subset of R-N (N > 2) be a C-2 bounded domain containing the origin 0. We study the behavior near 0 of positive solutions of equation (E) - Delta u + vertical bar x vertical bar(alpha)u(p) + vertical bar x vertical bar(beta) vertical bar del(U)vertical bar(q) = 0 in Omega\ {0} , where alpha > -2, beta > -1, p > 1, and q > 1. When 1 < p <(N+ alpha) / (N - 2) and 1 < q <(N+ beta) /(N - 1), we provide a full classification of positive solutions of (E) vanishing on partial derivative Omega. On the contrary, when p >= (N + alpha) /(N - 2) or(N + beta) /(N - 1) <= q <= 2 + beta, we show that any isolated singularity at 0 is removable.