On differentiability of solutions with respect to parameters in impulsive differential equations with adaptive state-dependent delay

In this paper we consider a class of impulsive nonlinear differential equations with adaptive state-dependent delays. We discuss well-posedness of the initial value problem under assumptions which imply the strict monotonicity of the delayed argument function. We show differentiability of the soluti...

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Bibliographic Details
Published in:Journal of Differential Equations 2024-12, Vol.413, p.751-804
Main Author: Hartung, Ferenc
Format: Article
Language:English
Subjects:
Adaptive delay
Delay differential equation
Differentiability with respect to parameters
Impulsive differential equation
State-dependent delay
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Summary:In this paper we consider a class of impulsive nonlinear differential equations with adaptive state-dependent delays. We discuss well-posedness of the initial value problem under assumptions which imply the strict monotonicity of the delayed argument function. We show differentiability of the solution with respect to some parameters in the equations including the initial function. This paper extends the techniques of earlier works to the case when impulsive condition is present.
ISSN:0022-0396
DOI:10.1016/j.jde.2024.09.003