an:05178758
Zbl 1123.35084
Ezzinbi, Khalil; Liu, James H.
Periodic solutions of some evolution equations with infinite delay
EN
Int. J. Evol. Equ. 2, No. 1, 19-27 (2007).
00192549
2007
j
35R10 35B10
measure of non-compactness; condensing map; partial functional differential equation with infinite delay; existence of periodic solutions; Hille-Yosida condition
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.