Asymptotic behaviour of ground states of quasilinear elliptic problems with two vanishing parameters, Part II

We study the pointwise asymptotic behavior of the radially symmetric ground state solution of a quasilinear elliptic equation involving the p-Laplacian in R^n with two competing parameters. We obtain the exact asymptotic behavior of the ground state, for any 1<p<n, both at the origin and outside the origin, when the equation tends to critical growth. We also obtain the ``equilibrium relation'' between the two parameters, so that when they both vanish according to this relation, ground states neither blow up nor vanish. The results of this paper complete the description begun by Gazzola and Serrin.