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Zeitschrift für Analysis und ihre Anwendungen

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Volume 34, Issue 4, 2015, pp. 459–475
DOI: 10.4171/ZAA/1549

Published online: 2015-10-29

Asymptotic Almost Periodicity to Some Evolution Equations

Rong-Nian Wang[1], Qiao-Min Xiang[2] and Yong Zhou[3]

(1) Shanghai Normal University, China
(2) South China University of Technology, Guangzhou, Guangdong, China
(3) Xiangtan University, Xiangtan, Hunan, China

In this paper, we introduce a new notion of semi-Lipschitz continuity for the class of asymptotically almost periodic functions and establish new existence theorems for asymptotically almost periodic mild solutions to some semi linear abstract evolution equations upon making some suitable assumptions. As one would expect, the results presented here would generalize and improve some recent results in this area.

Keywords: Abstract evolution equation, semi-Lipschitz continuity, asymptotic almost periodicity

Wang Rong-Nian, Xiang Qiao-Min, Zhou Yong: Asymptotic Almost Periodicity to Some Evolution Equations. Z. Anal. Anwend. 34 (2015), 459-475. doi: 10.4171/ZAA/1549