Periodic solutions to a class of quasi-variational evolution equations

Noriaki Yamazaki,Masahiro Kubo

doi:10.1016/j.jde.2023.11.027

Periodic solutions to a class of quasi-variational evolution equations

Noriaki Yamazaki, Masahiro Kubo

https://doi.org/10.1016/j.jde.2023.11.027

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Journal: Journal of Differential Equations

Publication Date: Dec 5, 2023

Affiliation: Kanagawa University, Wakayama University

#Class Of Nonlinear Evolution Equations #Subdifferential Operator + Show 8 more

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Abstract

We study a time-periodicity problem for a class of abstract nonlinear evolution equations associated with subdifferential operators depending on both time and the unknown. Assuming time-periodicity for the subdifferential operator, we prove the existence of a periodic solution using the abstract theory of time-dependent subdifferential evolution equations and its generalization. We provide application examples for quasilinear parabolic variational inequalities with time-periodic constraints of non-local time-delay or memory type depending on the unknown.

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