## Journal of Integral Equations and Applications

### Some new results on bounded solutions to a semilinear integro-differential equation in Banach spaces

#### Abstract

In this article, by a concept of Stepanov type $\mu$-pseudo almost automorphic functions developed recently, we investigate some new existence results on bounded solutions to a semilinear integro-differential equation in Banach spaces. We first establish a new composition theorem of such functions, and then we prove the main results via ergodicity and composition theorems of Stepanov type $\mu$-pseudo almost automorphic functions combined with theories of uniformly exponentially stable and strongly continuous family of operators. These bounded solutions can cover (weighted) pseudo almost automorphic solutions with a Stepanov type forcing term as special cases.

#### Article information

Source
J. Integral Equations Applications, Volume 27, Number 2 (2015), 153-178.

Dates
First available in Project Euclid: 9 September 2015

https://projecteuclid.org/euclid.jiea/1441790284

Digital Object Identifier
doi:10.1216/JIE-2015-27-2-153

Mathematical Reviews number (MathSciNet)
MR3395966

Zentralblatt MATH identifier
1325.45012

#### Citation

Chang, Yong-Kui; Wei, Xue-Yan; N'Guérékata, G.M. Some new results on bounded solutions to a semilinear integro-differential equation in Banach spaces. J. Integral Equations Applications 27 (2015), no. 2, 153--178. doi:10.1216/JIE-2015-27-2-153. https://projecteuclid.org/euclid.jiea/1441790284

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