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. # 2002 Elsevier Science (USA)

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We study superlinear elliptic boundary value problems with perturbed symmetries in domains which are invariant under the action of a group G. We give conditions on the growth of the nonlinearity which guarantee the existence of infinitely many G-invariant solutions. These conditions improve those obtained by Bahri and Lions (1988) and Bolle, Ghoussoub and Tehrani (2000) if the domain contains a G-orbit of large enough dimension.

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