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Periodic solutions to second-order differential equations with fading memory

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Abstract

We characterize existence and uniqueness of periodic strong and mild solutions to an abstract second order differential equation with memory in Banach spaces. Using vector-valued Fourier multipliers we give necessary and sufficient conditions in order to ensure the well-posedness of this equation in Lebesgue, Hölder and Besov spaces.

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Acknowledgements

The author thanks the reviewer for the detailed review and suggestions that have improved the previous version of the paper.

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  1. Instituto de Matemáticas, Universidad de Talca, Talca, Casilla, 747, Chile

    Rodrigo Ponce

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  1. Rodrigo Ponce
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Ponce, R. Periodic solutions to second-order differential equations with fading memory. Math. Z. 307, 5 (2024). https://doi.org/10.1007/s00209-024-03474-z

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