Rodríguez López, JorgePrecup, Radu2025-12-192025-12-192021Precup, R., Rodríguez-López, J. A Unified Variational Approach to Discontinuous Differential Equations. Mediterr. J. Math. 18, 62 (2021). https://doi.org/10.1007/s00009-021-01705-91660-5446https://hdl.handle.net/10347/44613A direct variational technique involving Clarke generalized gradient is used to treat general boundary value problems with discontinuous nonlinearities. Based on the theory of positive definite symmetric operators it is established the nonsmooth variational form of the regularized inclusions which give the Filippov solutions of the discontinuous problems. These solutions reduce to classical solutions in case that a transversality condition on the set of discontinuities is satisfied. The results apply to a wide class of concrete boundary value problems of different orders. Two illustrative examples are given.engCopyright © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer NatureNonsmooth critical point theorDiscontinuous differential equationMultivalued operatorjournal article1660-5454open access