Existence and asymptotic properties of singular solutions of nonlinear elliptic equations in Rn\{0}

We consider the following singular semilinear problem {Delta u(x) + p(x)u(gamma) = 0, x is an element of D (in the distributional sense), u > 0, in D, lim(vertical bar x vertical bar -> 0) vertical bar x vertical bar(n-2 )u(x) = 0, lim(vertical bar x vertical bar ->infinity) u(x) = 0, where gamma < 1, D = R-n \ {0} (n >= 3) and p is a positive continuous function in D, which may be singular at x = 0. Under sufficient conditions for the weighted function p(x), we prove the existence of a positive continuous solution on D, which could blow-up at the origin. The global asymptotic behavior of this solution is also obtained.