Journal of Integral Equations and Applications

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

Yong-Kui Chang, Xue-Yan Wei, and G.M. N'Guérékata

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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

Permanent link to this document
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

Subjects
Primary: 34K14: Almost and pseudo-periodic solutions 35B15: Almost and pseudo-almost periodic solutions 45N05: Abstract integral equations, integral equations in abstract spaces 58D25: Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]

Keywords
Stepanov type $\mu$-pseudo almost automorphic functions Integro-differential equations bounded solutions fixed point theorems

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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