Journal of Integral Equations and Applications

Asymptotically typed solutions to a semilinear integral equation

Yong-Kui Chang, Xiao-Xia Luo, and G.M. N'Guérékata

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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

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

First available in Project Euclid: 31 October 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K14: Almost and pseudo-periodic solutions 60H10: Stochastic ordinary differential equations [See also 34F05] 35B15: Almost and pseudo-almost periodic solutions 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]

$\mu$-pseudo almost automorphic function semilinear integral equations integral resolvent family fixed point


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.

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