Massera-type theorem for the existence of C-(n)-almost-periodic solutions for partial functional differential equations with infinite delay

作者：Ezzinbi Khalil; Fatajou Samir; N'guerekata Gaston Mandata^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2008, 69(4): 1413-1424.

DOI：10.1016/j.na.2007.06.041

• Hille-Yosida conditions
• infinite delay
• C-0-semigroup
• integral solutions
• fading memory space
• reduction principle
• C-(n)-almost-periodic solution
• exponential dichotomy

In this paper, We Study the existence of C-(n)-almost-periodic solutions for partial functional differential equations with infinite delay. We assume that the undelayed part is not necessarily densely defined and satisfies the Hille-Yosida condition. We use the reduction principle developed recently in [M. Adimy, K. Ezzinbi, A. Ouhinou, Variation of constants formula and almost-periodic Solutions for some partial functional differential equations with infinite delay, Journal of Mathematical Analysis and Applications 317 (2006) 668-689] to prove the existence of a C-(n)-almost-periodic Solution when there is at least one bounded Solution ill R+. We give an application to the Lotka-Volterra model with diffusion.

• 出版日期2008-8-15