Singular solutions of a nonlinear elliptic equation in a punctured domain

We consider the following semilinear problem {-Delta u (x) = a (x) u(sigma) (x), x is an element of Omega\{0} (in the distributional sense), u > 0, in Omega\{0}, lim(vertical bar x vertical bar -> 0) vertical bar x vertical bar(n-2) u (x) = 0, u (x) - 0, x is an element of partial derivative Omega, where sigma < 1, Omega is a bounded regular domain in R-n (n >= 3) containing 0 and a is a positive continuous function in Omega\{0}, which may be singular at x = 0 and/or at the boundary partial derivative Omega. When the weight function a ( x) satisfies suitable assumption related to Karamata class, we prove the existence of a positive continuous solution on <(Omega)over bar>\{0}, which could blow-up at the origin. The global asymptotic behavior of this solution is also obtained.