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Periodic solutions of some evolution equations with infinite delay. (English) Zbl 1123.35084
Summary: We study the existence of periodic solutions for some partial functional differential equations with infinite delay. We assume that the linear part is not necessarily densely defined and satisfies the Hille-Yosida condition, and the phase space is chosen to be \(C_g\) for some decreasing function \(g\) from \((-\infty,0]\) to \([1,\infty)\). We also present a related Massera type result, namely the existence of a bounded solution on \(\mathbb{R}^+\) implies the existence of a periodic solution.

MSC:
35R10 Functional partial differential equations
35B10 Periodic solutions to PDEs
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