Positive evanescent solutions of singular elliptic problems in exterior domains

We investigate the existence of positive solutions for the following class of nonlinear elliptic problems div (a(parallel to x parallel to)del u (x)) + f (x, u (x)) - (u (x))(-alpha)parallel to del u (x)parallel to(beta) + g (parallel to x parallel to)x . del u (x) = 0, where X I R-n and parallel to x parallel to > R, with the condition lim(x) = 0. We present the approach based on the subsolution and supersolution method for bounded subdomains and a certain convergence procedure. Our results cover both sublinear and superlinear cases of f. The speed of decaying of solutions will be also characterized more precisely.