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Well‐posedness of second order differential equations with memory

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  • Rodrigo Ponce

Abstract

In this paper we give characterizations of the existence and uniqueness of Hölder continuous solutions of certain abstract integro‐differential equation with memory in terms of a resolvent operator. Moreover, we give necessary conditions in order to ensure the existence and uniqueness of mild solutions on the real line.

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  • Rodrigo Ponce, 2022. "Well‐posedness of second order differential equations with memory," Mathematische Nachrichten, Wiley Blackwell, vol. 295(11), pages 2246-2264, November.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:11:p:2246-2264
    DOI: 10.1002/mana.202000113
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    References listed on IDEAS

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    1. Rodrigo Ponce & Verónica Poblete, 2017. "Maximal L p -regularity for fractional differential equations on the line," Mathematische Nachrichten, Wiley Blackwell, vol. 290(13), pages 2009-2023, September.
    2. Gang Cai & Shangquan Bu, 2016. "Well-posedness of second order degenerate integro-differential equations with infinite delay in vector-valued function spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 289(4), pages 436-451, March.
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