New composition theorems of Stepanov-like weighted pseudo almost automorphic functions and applications to nonautonomous evolution equations
type: Item
instance of: scholarly article
title: New composition theorems of Stepanov-like weighted pseudo almost automorphic functions and applications to nonautonomous evolution equations
zbMATH Open document ID: 1316.34064
author: Rui Zhang
author: Yong Kui Chang
author: G. M. N'Guérékata
published in: Nonlinear Analysis. Real World Applications
publication date: 2012-12-28T00:00:00Z
review text: This paper deals with the following non-autonomous evolution equation: \[ u'(t)=A(t)u(t)+f(t,u(t)),\,\, t\in \mathbb{R},\tag{1} \] where \(A(t)\) satisfies the ``Acquistapace-Terreni'' condition, and generates an evolution family \((U(t,s))_{t\geq s}\) with exponential dichotomy. The function \(f:\mathbb{R}\times \mathbb{X}\to \mathbb{X}\) is a Stepanov-like weighted pseudo almost automorphic function. The authors start by proving some new composition theorems of Stepanov-like weighted pseudo almost automorphic function. Then under suitable conditions on \(f\), they prove the existence and uniqueness of solution of (1). The results are obtained by means of Banach fixed point theorem. An example is also given to illustrate the main results.
reviewed by: Gisèle M. Mophou
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 43A60
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6118825
zbMATH Keywords: composition theorem
zbMATH Keywords: Stepanov-like weighted pseudo almost automorphic
zbMATH Keywords: nonautonomous evolution equations
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2012.04.016
OpenAlex ID: W2007857242
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DOI: 10.1016/J.NONRWA.2012.04.016
description: scientific article; zbMATH DE number 6118825