Perturbations of nonsmooth symmetric nonlinear eigenvalue problems

We consider a symmetric semilinear boundary value problem having infinitely many solutions. We prove that, if we perturb this problem in a non-symmetric way, then the number of solutions goes to infinity as the perturbation tends to zero. The growth conditions on the nonlinearities do not ensure the smoothness of the associated functional. (C) 1999 Academie des Sciences / Editions scientifiques et medicales Elsevier SAS.