Nonlocal differential equations with multivalued perturbations in Banach spaces
type: Item
instance of: scholarly article
title: Nonlocal differential equations with multivalued perturbations in Banach spaces
zbMATH Open document ID: 1163.34041
author: Lanping Zhu
author: Gang Li
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2008-10-21T00:00:00Z
review text: The authors study the following nonlocal initial value problem \[ \begin{cases} u'(t)\in Au(t)+F(t,u(t)),&\;t\in[0,T],\\ u(0)=g(u),\end{cases} \] where \(A:D(A)\subseteq E\rightarrow E\) is the densely defined generator of a compact semigroup for \(t>0\) in a real Banach space \(E\); \(F\) is an upper-Carathéodory multifunction; \(g:C([0,T])\rightarrow E\) is a given function. As the main result, a theorem on the existence of mild solutions for this problem is proved. An example illustrating the abstract result is also presented.
reviewed by: Paola Rubbioni
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 5355031
zbMATH Keywords: nonlocal differential inclusions
zbMATH Keywords: upper-Carathéodory multifunctions
zbMATH Keywords: mild solutions
zbMATH Keywords: compact semigroup
MaRDI profile type: Publication
full work available at URL: j.na.2007.08.057
OpenAlex ID: W1974864858
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DOI: 10.1016/J.NA.2007.08.057
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description: scientific article; zbMATH DE number 5355031