  In this work we prove some abstract results about the existence of a
minimizer for locally Lipschitz functionals, without any assumption of
homogeneity, over a set which has its definition inspired in the Nehari
manifold. As applications we present a result of existence of ground state
bounded variation solutions of problems involving the 1-Laplacian and the
mean-curvature operator, where the nonlinearity satisfies mild assumptions.

Analysis of PDEs