RT info:eu-repo/semantics/article
T1 Topologies of continuity for Carathéodory delay differential equations with applications in non-autonomous dynamics
A1 Longo, Iacopo Paolo
A1 Novo, Sylvia
A1 Obaya, Rafael
K1 Carathéodory functions, non-autonomous Carathéodory differential equations, continuous dependence on initial data, linearized skew-product semiflow.
AB We study some already introduced and some new strong and weak topologies of integral type to provide continuous dependence on continuous initial data for the solutions of non-autonomous Carathéodory delay differential equations. As a consequence, we obtain new families of continuous skew-product semiflows generated by delay differential equations whose vector fields belong to such metric topological vector spaces of Lipschitz Carathéodory functions. Sufficient conditions for the equivalence of all or some of the considered strong or weak topologies are also given. Finally, we also provide results of continuous dependence of the solutions as well as of continuity of the skew-product semiflows generated by Carathéodory delay differential equations when the considered phase space is a Sobolev space.
PB American Institute of Mathematical Sciences
SN 1553-5231
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/40204
UL http://uvadoc.uva.es/handle/10324/40204
LA eng
NO Discrete and Continuous Dynamical Systems, 2019, vol. 39, no. 9, p. 5491-5520
NO Producción Científica
DS UVaDOC
RD 18-dic-2024