Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions
Figueiredo, Giovany M.
Pimenta, Marcos T. O. [UNESP]
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In this work we prove some abstract results about the existence of a minimizer for locally Lipschitz functionals, 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 1-biharmonic operator, where the nonlinearity satisfies mild assumptions.
1-Biharmonic, 1-Laplacian, Bounded variation functions, Nehari method
Nonlinear Differential Equations and Applications, v. 25, n. 5, 2018.