Stability analysis for nonlocal evolution equations involving infinite delays
type: Item
instance of: scholarly article
title: Stability analysis for nonlocal evolution equations involving infinite delays
author: Van Dac Nguyen
author: Nguyen Nhu Thang
author: Dinh-Ke Tran
published in: Journal of Fixed Point Theory and Applications
publication date: 2022-12-20T00:00:00Z
review text: The aim of this paper is to study the well-posedness and stability for some nonlocal evolution equations with infinite delay. The phase space is axiomatically defined and the linear part A is self-adjoint on a Hilbert space. Firstly, the authors used the resolvent operator theory to define the variation of constants formula for the mild solutions. If the resolvent of A is compact, the authors proved the existence of a mild solution by using Schauder's fixed point theorem. When the nonlinearity is locally Lipschitz the authors proved the uniqueness of the mild solution. Secondly, the authors used the Halanay type inequality to prove the asymptotic stability and weak asymptotic stability.
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K38
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7634924
zbMATH Keywords: nonlocal differential equation
zbMATH Keywords: mild solution
zbMATH Keywords: asymptotic stability
zbMATH Keywords: weak stability
reviewed by: Khalil Ezzinbi
MaRDI profile type: Publication
full work available at URL: s11784-022-01007-x
OpenAlex ID: W4311772784
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DOI: 10.1007/S11784-022-01007-X
description: scientific article; zbMATH DE number 7634924