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 $\lambda$ and $\mu$, 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 $\lambda$ and $\mu$ 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.