Abstract
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.
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Acknowledgements
We would like to warmly thank Prof. Olimpio Hiroshi Miyagaki for several discussions about this subject. We also would like to thank the anonymous referees by careful reading this text. This work was written while Giovany M. Figueiredo was as a Visiting Professor at FCT—Unesp in Presidente Prudente—SP. He would like to thanks the warm hospitality.
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Marcos T. O. Pimenta is supported by Fapesp 2017/01756-2 and CNPq 442520/2014-0. Giovany M. Figueiredo is supported by CNPq and Fapesp.
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Figueiredo, G.M., Pimenta, M.T.O. Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions. Nonlinear Differ. Equ. Appl. 25, 47 (2018). https://doi.org/10.1007/s00030-018-0538-2
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DOI: https://doi.org/10.1007/s00030-018-0538-2