Translator Disclaimer
SUMMER 2015 Some new results on bounded solutions to a semilinear integro-differential equation in Banach spaces
Yong-Kui Chang, Xue-Yan Wei, G.M. N'Guérékata
J. Integral Equations Applications 27(2): 153-178 (SUMMER 2015). DOI: 10.1216/JIE-2015-27-2-153

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.

Citation

Download Citation

Yong-Kui Chang. Xue-Yan Wei. G.M. N'Guérékata. "Some new results on bounded solutions to a semilinear integro-differential equation in Banach spaces." J. Integral Equations Applications 27 (2) 153 - 178, SUMMER 2015. https://doi.org/10.1216/JIE-2015-27-2-153

Information

Published: SUMMER 2015
First available in Project Euclid: 9 September 2015

zbMATH: 1325.45012
MathSciNet: MR3395966
Digital Object Identifier: 10.1216/JIE-2015-27-2-153

Subjects:
Primary: 34K14, 35B15, 45N05, 58D25

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.27 • No. 2 • SUMMER 2015
Back to Top