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Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces |
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| Authors: | Hui-Sheng Ding Ti-Jun Xiao |
| Institution: | a College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, People’s Republic of China b Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China c Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China |
| Abstract: | This paper is concerned with almost automorphy of the solutions to a nonautonomous semilinear evolution equation u′(t)=A(t)u(t)+f(t,u(t)) in a Banach space with a Stepanov-like almost automorphic nonlinear term. We establish a composition theorem for Stepanov-like almost automorphic functions. Furthermore, we obtain some existence and uniqueness theorems for almost automorphic solutions to the nonautonomous evolution equation, by means of the evolution family and the exponential dichotomy. Some results in this paper are new even if A(t) is time independent. |
| Keywords: | 43A60 34G20 |
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