Infinitely many solutions for quasilinear elliptic equations with lack of symmetry

In this paper we look for weak solutions of a quasilinear elliptic model problem with Dirichlet boundary conditions on a bounded domain. We prove that under suitable assumptions infinitely many solutions exist in spite of the lack of symmetry. A suitable supercritical growth is allowed for the nonlinear term. We use a variant of the variational perturbation techniques introduced by Rabinowitz but by means of a weak version of the Cerami-Palais-Smale condition.