Nonlinear delay equations with nonautonomous past

Genni Fragnelli; Dimitri Mugnai

doi:10.3934/dcds.2008.21.1159

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2008, Volume 21, Issue 4: 1159-1183. Doi: 10.3934/dcds.2008.21.1159

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Nonlinear delay equations with nonautonomous past

Genni Fragnelli^1, and
Dimitri Mugnai^2,

1.
Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Siena, Via Roma 56, 53100 Siena
2.
Dipartimento di Matematica e Informatica, Universita di Perugia, 06123 Perugia

Received: May 31, 2007

Revised: February 29, 2008

Published: September 2008

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Abstract

Inspired by a biological model on genetic repression proposed by P. Jacob and J. Monod, we introduce a new class of delay equations with nonautonomous past and nonlinear delay operator. With the aid of some new techniques from functional analysis we prove that these equations, which cover the biological model, are well--posed.

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Mathematics Subject Classification: Primary: 34G20, 47A10; Secondary: 47D06, 47H20, 47N60.

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