November  2008, 21(4): 1159-1183. doi: 10.3934/dcds.2008.21.1159

Nonlinear delay equations with nonautonomous past

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  June 2007 Revised  March 2008 Published  April 2008

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.
Citation: Genni Fragnelli, Dimitri Mugnai. Nonlinear delay equations with nonautonomous past. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1159-1183. doi: 10.3934/dcds.2008.21.1159
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