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Resolvent of nonautonomous linear delay functional differential equations

2015; De Gruyter Open; Volume: 2; Issue: 1 Linguagem: Inglês

10.1515/msds-2015-0006

2353-0626

Joël Blot, Mamadou Ibrahima Koné,

Advanced Mathematical Modeling in Engineering

Abstract The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.