Rodríguez López, JorgeTomeček, Jan2024-05-062024-05-062024Journal of Mathematical Analysis and Applications, Volume 536, Issue 1, 2024, 1282370022-247Xhttp://hdl.handle.net/10347/33786e present an existence principle for boundary value problems involving discontinuous ordinary differential equations of the second order using the Krasovskii regularization technique. Especially we obtain sufficient conditions of transversality type for Krasovskii solutions to be also Carathéodory solutions of the original problem. This result is applied on a certain billiard problem, which can be thought as an ordinary differential equation with state-dependent impulses that is equivalent to certain discontinuous differential equation. In particular, we obtain new existence and multiplicity results for Dirichlet problems in billiard spaces with time-varying boundariesengAttribution-NonCommercial-NoDerivatives 4.0 Internacional© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)http://creativecommons.org/licenses/by-nc-nd/4.0/Discontinuous differential equationsDifferential inclusionsImpulsive differential equationsBilliard problemMultiple solutionsDirichlet problemjournal article10.1016/j.jmaa.2024.128237open access