Singular solutions for semilinear elliptic equations with general supercritical growth

A positive radial singular solution for Delta u + f (u) = 0 with a general supercritical growth is constructed. An exact asymptotic expansion as well as its uniqueness in the space of radial functions are also established. These results can be applied to the bifurcation problem Delta u + lambda f (u) = 0 on a ball. Our method can treat a wide class of nonlinearities in a unified way, e.g., u(p) log u, exp(u(p)) and exp(center dot center dot center dot exp(u)center dot center dot center dot) as well as u(p) and e(u). Main technical tools are intrinsic transformations for semilinear elliptic equations and ODE techniques.