Bifurcation and asymptotic analysis for a class of supercritical elliptic problems in an exterior domain
Francesca Gladiali, Filomena Pacella · Nonlinearity · 2011
We consider the problem either in an annulus A R or in the domain , N ⩾ 3, and . We prove that the unique radial solution u p , R in A R converges, as R → + ∞ , to the unique fast-decay radial solution in Ω and show several related asymptotic estimates, in particular spectral convergence. Analogous asymptotic estimates are also proved for nonradial uniformly bounded solutions in A R . From this we deduce that bifurcation of nonradial solutions occurs at the fast-decay degenerate radial solutions of the problem in Ω 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 40 295–317).