Three solutions for a Dirichlet problem with one-sided growth conditions on the nonlinearities

We consider a semilinear elliptic partial differential equation, depending on two positive parameters λλ and μμ, coupled with homogeneous Dirichlet boundary conditions. Assuming only one-sided growth conditions on the nonlinearities involved, we prove the existence of at least three weak solutions for λλ and μμ lying in convenient intervals. We employ techniques of nonsmooth analysis introduced by Degiovanni and Zani, and a theorem of Ricceri for multiplicity of local minimizers.