## Journal of Integral Equations and Applications

### Asymptotically typed solutions to a semilinear integral equation

#### Abstract

In this paper, we investigate the existence of $\mu$-pseudo almost automorphic solutions to the semilinear integral equation $x(t)=\int_{-\infty}^{t}a(t-s)[Ax(s)+f(s,x(s))]\,ds$, $t\in\mathbf{R}$ in a Banach space $\mathbf{X}$, where $a\in L^{1}(\mathbf{R}_{+})$, $A$ is the generator of an integral resolvent family of linear bounded operators defined on the Banach space $\mathbf{X}$, and $f:\mathbf{R}\times\mathbf{X}\rightarrow\mathbf{X}$ is a $\mu$-pseudo almost automorphic function. The main results are proved by using integral resolvent families combined with the theory of $\mu$-pseudo almost automorphic functions.

#### Article information

Source
J. Integral Equations Applications, Volume 26, Number 3 (2014), 323-343.

Dates
First available in Project Euclid: 31 October 2014

https://projecteuclid.org/euclid.jiea/1414761101

Digital Object Identifier
doi:10.1216/JIE-2014-26-3-323

Mathematical Reviews number (MathSciNet)
MR3273898

Zentralblatt MATH identifier
1326.45004

#### Citation

Chang, Yong-Kui; Luo, Xiao-Xia; N'Guérékata, G.M. Asymptotically typed solutions to a semilinear integral equation. J. Integral Equations Applications 26 (2014), no. 3, 323--343. doi:10.1216/JIE-2014-26-3-323. https://projecteuclid.org/euclid.jiea/1414761101