Asymptotic almost periodicity to some evolution equations
type: Item
instance of: scholarly article
title: Asymptotic almost periodicity to some evolution equations
zbMATH Open document ID: 1373.34068
DOI: 10.4171/ZAA/1549
author: Rong-Nian Wang
author: Qiao-Min Xiang
author: Yong Zhou
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2015-11-17T00:00:00Z
review text: After introducing a new property of semi-Lipschitz continuity for a class of asymptotic almost periodic functions and without imposing the Lipschitz condition on the nonlinear term, the authors study the existence of asymptotically almost periodic mild solution to some class of autonomous semilinear evolution equations of the form: \[ u'(t) = A u(t) + f(t,u(t)),\quad t \in \mathbb{R} \] in a Banach space \(\mathbb{X},\) where \(A:D(A)\subset \mathbb{X} \to \mathbb{X}\) is the infinitesimal generator of a hyperbolic \(C_{0}-\)semigroup, \(f: \mathbb{R} \times \mathbb{X} \to \mathbb{X}\) is semi-Lipschitz continuous, and \[ \frac{d}{dt}\big[u(t) - h(t,u(t))\big] = Au(t) + f(t, u(t)),\quad t \in \mathbb{R}, \] where \(A:D(A)\subset \mathbb{X} \to \mathbb{X}\) is the infinitesimal generator of a compact analytic semigroup such that \(0\in \rho(A)\) and \(h: \mathbb{R} \times \mathbb{X} \to \mathbb{X_{\alpha}}\) satisfies some appropriate conditions.
reviewed by: Mohamed Zitane
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 6510074
zbMATH Keywords: abstract evolution equation
zbMATH Keywords: semi-Lipschitz continuity
zbMATH Keywords: asymptotic almost periodicity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6510074