Almost automorphic solutions of nonautonomous evolution equations |
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Authors: | Hui-Sheng Ding, Wei Long,Gaston M. N Gu r kata |
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Affiliation: | aCollege of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, People’s Republic of China;bDepartment of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA |
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Abstract: | In this paper, we establish some new theorems about the existence of almost automorphic solutions to nonautonomous evolution equations u′(t)=A(t)u(t)+f(t) and u′(t)=A(t)u(t)+f(t,u(t)) in Banach spaces. As we will see, our results allow for a more general A(t) to some extent. An example is also given to illustrate our results. In addition, by means of an example, we show that one cannot ensure the existence of almost automorphic solutions to u′(t)=A(t)u(t)+f(t) even if the evolution family U(t,s) generated by A(t) is exponentially stable and fAA(X). |
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Keywords: | Almost automorphic Nonautonomous evolution equations Evolution family Exponential dichotomy |
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