RT Journal Article
T1 Second–order discontinuous ODEs and billiard problems
A1 Rodríguez López, Jorge
A1 Tomeček, Jan
K1 Discontinuous differential equations
K1 Differential inclusions
K1 Impulsive differential equations
K1 Billiard problem
K1 Multiple solutions
K1 Dirichlet problem
AB e 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 boundaries
PB Elsevier
SN 0022-247X
YR 2024
FD 2024
LK http://hdl.handle.net/10347/33786
UL http://hdl.handle.net/10347/33786
LA eng
NO Journal of Mathematical Analysis and Applications, Volume 536, Issue 1, 2024, 128237
NO Jorge Rodríguez–López was partially supported by Agencia Estatal de Investigación, Spain, and Feder, Project PID2020-113275GB-I00. Jan Tomeček was supported by Palacký University in Olomouc (grant no. IGA_PrF_2023_009)
DS Minerva
RD 27 abr 2026