On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays

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10 Citations (Scopus)

Abstract

In this paper, we consider a class of nonlinear neutral differential equations with state-dependent delays in both the neutral and the retarded terms. We study well-posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the C-norm.

Original languageEnglish
Pages (from-to)17-47
Number of pages31
JournalAnnali di Matematica Pura ed Applicata, Series 4
Volume192
Issue number1
DOIs
Publication statusPublished - 2013

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State-dependent Delay
Neutral Differential Equation
Differentiability
Differential equations
Continuous Dependence
Well-posedness
Nonlinear Differential Equations
Norm
Term
Class

Keywords

  • Differentiability with respect to parameters
  • Neutral differential equation
  • State-dependent delay

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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abstract = "In this paper, we consider a class of nonlinear neutral differential equations with state-dependent delays in both the neutral and the retarded terms. We study well-posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the C-norm.",
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AB - In this paper, we consider a class of nonlinear neutral differential equations with state-dependent delays in both the neutral and the retarded terms. We study well-posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the C-norm.

KW - Differentiability with respect to parameters

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KW - State-dependent delay

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