RT Journal Article
T1 Existence and uniqueness of solutions for systems of discontinuous differential equations under localized Bressan-Shen transversality conditions
A1 López Pouso, Rodrigo
A1 Rodríguez López, Jorge
K1 Discontinuous differential equations
K1 Existence
K1 Uniqueness
AB We present new results on existence and uniqueness of absolutely continuous solutions for systems of discontinuous ordinary differential equations. Our existence result complements an earlier theorem by Bressan and Shen. Basically, we show that a global transversality condition assumed by Bressan and Shen need only be imposed on the sets where the nonlinear part is discontinuous. Our proof, completely different to the one given by Bressan and Shen, uses Krasovskij solutions as a first step. We illustrate the applicability of our result with several examples not covered by the previous literature. The second part of this paper concerns uniqueness. Specifically, we prove uniqueness of solutions for discontinuous systems of differential equations with piecewise Lipschitz continuous nonlinearities and assuming localized Bressan–Shen transversality conditions on the boundaries between different Lipschitz continuity domains. Our uniqueness result appears to be new even in the classical case of continuous nonlinearities.
PB Elsevier
SN 1096-0813
YR 2020
FD 2020
LK https://hdl.handle.net/10347/44801
UL https://hdl.handle.net/10347/44801
LA eng
NO Journal of Mathematical Analysis and Applications Volume 492, Issue 1, 1 December 2020, 124425
NO Rodrigo López Pouso was partially supported by Ministerio de Economía y Competitividad, Spain, and FEDER, Project MTM2016-75140-P. Jorge Rodríguez–López was financially supported by Xunta de Galicia Scholarship ED481A-2017/178.
DS Minerva
RD 8 jun 2026