Almost periodic solutions of periodic linear partial functional differential equations

Vu Trong Luong; Nguyen Van Minh

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arXiv · 1807.03826

Almost periodic solutions of periodic linear partial functional differential equations

Vu Trong Luong·Nguyen Van Minh

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Abstract

We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$. The main conditions are stated in terms of the spectrum of the monodromy operator associated with the equation and the frequencies of the forcing term $f$. The obtained results extend recent results on the subject. A discussion on how the results could be extended to the case when $A$ depends on $t$ is given.

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Vu Trong Luong, Nguyen Van Minh. 2018-07-10. Almost periodic solutions of periodic linear partial functional differential equations. https://arxiv.org/abs/1807.03826

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