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FALL 2014 Asymptotically typed solutions to a semilinear integral equation
Yong-Kui Chang, Xiao-Xia Luo, G.M. N'Guérékata
J. Integral Equations Applications 26(3): 323-343 (FALL 2014). DOI: 10.1216/JIE-2014-26-3-323


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.


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Yong-Kui Chang. Xiao-Xia Luo. G.M. N'Guérékata. "Asymptotically typed solutions to a semilinear integral equation." J. Integral Equations Applications 26 (3) 323 - 343, FALL 2014.


Published: FALL 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1326.45004
MathSciNet: MR3273898
Digital Object Identifier: 10.1216/JIE-2014-26-3-323

Primary: 34F05 , 34K14 , 35B15 , 60H10

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

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.26 • No. 3 • FALL 2014
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