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BanachJ.Math.Anal.8(2014),no.2,49–59 L B -MAXIMALREGULARITYOFDEGENERATEDELAYEQUATIONSWITHPERIODICCONDITIONS J M A

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Banach J. Math. Anal. 8 (2014), no. 2, 49–59

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anach

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ournal of

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athematical

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nalysis ISSN: 1735-8787 (electronic)

www.emis.de/journals/BJMA/

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-MAXIMAL REGULARITY OF DEGENERATE DELAY EQUATIONS WITH PERIODIC CONDITIONS

SHANGQUAN BU Communicated by R. E. Curto

Abstract. Under suitable assumptions on the delay operatorF, we give nec- essary and sufficient conditions for the inhomogeneous abstract degenerate de- lay equations: (M u)0(t) = Au(t) +F ut+f(t), (t ∈ T) to haveLp-maximal regularity.

Department of Mathematical Science, University of Tsinghua, Beijing 100084, China.

E-mail address: [email protected]

Date: Received: May 21, 2013; Accepted: Sep. 8, 2013.

2010Mathematics Subject Classification. Primary 47D06; Secondary 34G10, 34K30, 43A15.

Key words and phrases. Maximal regularity, degenerate equations, delay equations.

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