Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations
type: Item
instance of: scholarly article
title: Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations
zbMATH Open document ID: 1169.34330
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-12-16T00:00:00Z
review text: Let \(X\) be a Banach space, and \(p\geq 1.\) The author proves the existence and uniqueness of a pseudo-almost periodic mild solution to the nonautonomous differential equation \[ u'(t)=A(t)u(t)+f(t),\quad t\in\mathbb R, \] where \(A(t):D(A(t))\subset X\rightarrow X\) is a family of densely defined closed linear operators with a common domain \(D=D(A(t)),\) independent of \(t,\) whose associated evolution family of operators is asymptotically stable, and \(f:R\rightarrow X\) is a continuous and Stepanov-like pseudo-almost periodic (or \(S^{p}\)-pseudo-almost periodic) function. This notion of \(S^{p}\)-pseudo-almost periodicity was introduced by the author [Commun. Math. Anal. 3, No.~1, 9--18 (2007; Zbl 1286.44007)], and generalizes the classical notion of pseudo-almost periodicity due to \textit{C. Y. Zhang} [J. Math. Anal. Appl. 181, No.~1, 62--76 (1994; Zbl 0796.34029) and 192, No.~2, 543--561 (1995; Zbl 0826.34040)].
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 42A75
zbMATH DE Number: 5382857
zbMATH Keywords: almost periodic
zbMATH Keywords: pseudo-almost periodic
zbMATH Keywords: Stepanov-like pseudo-almost periodicity
zbMATH Keywords: evolution family of operators
zbMATH Keywords: mild solution
zbMATH Keywords: Bochner transform
author: Toka Diagana
reviewed by: Behzad Djafari Rouhani
MaRDI profile type: Publication
full work available at URL: j.na.2007.10.051
OpenAlex ID: W2060035950
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DOI: 10.1016/J.NA.2007.10.051
description: scientific article; zbMATH DE number 5382857