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

Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions