Electron. J. Differential Equations, Vol. 2018 (2018), No. 37, pp. 1-16.

Existence of asymptotically almost automorphic mild solutions for nonautonomous semilinear evolution equations

Junfei Cao, Zaitang Huang, Gaston M. N'Guerekata

In this article, we study the existence of asymptotically almost automorphic mild solutions for a class of nonautonomous semilinear evolution equations and extend some related results in this direction. The working tools are based on the Krasnoselskii's fixed point theorem and compactness criterion. Finally, an example is presented to illustrate the main findings.

Submitted November 1, 2017. Published January 30, 2018.
Math Subject Classifications: 34K14, 35K90.
Key Words: Nonautonomous semilinear evolution equation; asymptotic almost automorphy; compact semigroup.

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  Junfei Cao
Department of Mathematics
Guangdong University of Education
Guangzhou 510303, China
email: jfcaomath@163.com, caojunfei@gdei.edu.cn
  Zaitang Huang
School of Mathematical Sciences
Guangxi Teachers Education University
Nanning 530023, China
email: zaitanghuang@163.com
Gaston M. N'Guerekata
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu, nguerekata@aol.com

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