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arXiv · 1705.00926

Topologies of $L^p_{loc}$ type for Carathéodory functions with applications in non-autonomous differential equations

Iacopo P. Longo·Sylvia Novo·Rafael Obaya
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Abstract

Metric topological vector spaces of Carathéodory functions and topologies of $L^p_{loc}$ type are introduced, depending on a suitable set of moduli of continuity. Theorems of continuous dependence on initial data for the solutions of non-autonomous Carathéodory differential equations are proved in such new topological structures. As a consequence, new families of continuous linearized skew-product semiflows are provided in the Carathéodory spaces.

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Iacopo P. Longo, Sylvia Novo, Rafael Obaya. 2017-08-11. Topologies of $L^p_{loc}$ type for Carathéodory functions with applications in non-autonomous differential equations. https://doi.org/10.1016/j.jde.2017.08.006

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