A Dirichlet inclusion problem on Finsler manifolds

Abstract

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.