  In this paper we study a Dirichlet-type differential inclusion involving the
Finsler-Laplace operator on a complete Finsler manifold. Depending on the
positive $\lambda$ parameter of the inclusion, we establish non-existence, as
well as existence and multiplicity results by applying non-smooth variational
methods. The main difficulties are given by the problem's highly nonlinear
nature due to the general Finslerian setting, as well as the nonsmooth context.
