A Dirichlet inclusion problem on Finsler manifolds

In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator defined on a complete Finsler manifold. Depending on the positive $\lambda$ parameter of the problem, we establish non-existence, as well as existence and multiplicity results by applying non-smooth variational methods. The article’s significance is given by the synthesis of the non-smooth context with the highly nonlinear problem inherent in the general Finslerian framework.