Bifurcation and asymptotic analysis for a class of supercritical elliptic problems in an exterior domain

We consider the problem {-δ u = up u > 0 u = 0 either in an annulus AR or in the domain ω = ℝN B̄, N ≥ 3, B = {x ε ℝN , |x| < 1} and p > 2N/ N-2 . We prove that the unique radial solution up,R in AR converges, as R → +∞, to the unique fast-decay radial solution in and showseveral related asymptotic estimates, in particular spectral convergence. Analogous asymptotic estimates are also proved for nonradial uniformly bounded solutions in AR. From this we deduce that bifurcation of nonradial solutions occurs at the fast-decay degenerate radial solutions of the problem in - and that the bifurcation branches are limits, in a suitable sense, of the bifurcation branches already found in (Gladiali et al 2011 Calc. Var. Partial Diff. Eqns 40 295317). © 2011 IOP Publishing Ltd & London Mathematical Society.