Linking–Preserving Perturbations of Symmetric Functionals

We consider paths of functionals starting with one which is invariant under the action of an arbitrary group of symmetries. We give conditions for the existence of an unbounded sequence of critical values of the non-symmetric functional at the end of the path in terms of the growth of the critical values of the symmetric one. We apply this to obtain a multiplicity result for a system of elliptic equations whose symmetries are perturbed by a linear term and a non-homogeneous boundary condition.