Three Nontrivial Solutions for a Quasilinear Elliptic Differential Equation at Resonance with Discontinuous Right Hand Side

We study a quasilinear elliptic equation at resonance with discontinuous right hand side. To have an existence theory, we pass to a multivalued version of the problem by filling in the gaps at the discontinuity points. Using the nonsmooth critical point theory of Chang for locally Lipschitz functionals and the Ekeland variational principle, we show that the resulting elliptic inclusion has three distinct nontrivial solutions.