Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 35, pp. 1-11.

Title: Massera type theorems for abstract non-autonomous evolution equations

Authors: Lan-Ling Zheng (Jiangxi Normal Univ., Nanchang, Jiangxi, China)
         Hui-Sheng Ding (Jiangxi Normal Univ., Nanchang, Jiangxi, China)

Abstract: 
We establish two fixed point theorems for affine maps in Banach spaces, 
with weaker assumptions than those in the literature. 
Then we establish some  Massera type results for  abstract linear evolution 
equations without assuming the existence of 
bounded solutions,  which is an indispensable condition in the classical Massera 
theorem and in the earlier literature.
As application, we present an existence result on periodic mild solutions to 
abstract nonautonomous semilinear evolution equations.


Submitted October 8, 2023.  Published June 06, 2024.
Math Subject Classifications: 34C25, 35B10, 34G10, 47D06.
Key Words: Massera theorem; affine map; periodic solution; abstract evolution.