Periodic solutions of some evolution equations with infinite delay. (English) Zbl 1123.35084

Ezzinbi, Khalil; Liu, James H.

Int. J. Evol. Equ. 2, No. 1, 19-27 (2007).

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

Keywords:

measure of non-compactness; condensing map; partial functional differential equation with infinite delay; existence of periodic solutions; Hille-Yosida condition