SYMMETRY-BREAKING AT NONPOSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC-EQUATIONS

We consider symmetry-breaking bifurcations at non-positive, radially s ymmetric solutions of semilinear elliptic equations on a ball with Dir ichlet boundary conditions. For nonlinearities which are asymptoticall y affine linear, we find solutions at which the symmetry breaks. The k ernel of the linearized equation at these solutions is an absolutely i rreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the af fine linear problem is small enough. Thus-we obtain, by the equivarian t branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.