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In this paper we consider a class of differential equations with state-dependent delays. We show differentiability of the solution with respect to the initial function and the initial time for each fixed time value assuming that the state-dependent time lag function is piecewise monotone increasing. Based on these results, we prove a nonlinear variation of constants formula for differential equations with state-dependent delay. As an application, we discuss asymptotic properties of perturbed nonlinear differential equations with state-dependent delays. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the $$C$$ C -norm on the state-space, assuming that the state-dependent time lag function is piecewise strictly monotone. [ABSTRACT FROM AUTHOR]