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In this paper we consider a class of nonlinear neutral functional differential equations with state-dependent delays. We study well-posedness and differentiability of the solution with respect to the parameters in a pointwise sense and also in the supremum norm. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of delay differential equations of the form x(t) = α(t)h(x(t - τ), x(t - σ)) - β(t) f (x(t)), where h is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of functional differential equations with time-dependent delay. We show continuous differentiability of the solution with respect to the time delay function for each fixed time value assuming natural conditions on the delay function. As an application of the differentiability result, we give a numerical study to estimate the time delay function using the quasilinearization method. [ABSTRACT FROM AUTHOR]