Abstract
This chapter describes asymptotically autonomous neutral functional differential equations with time-dependent lag. The aim is to extend, for a system of functional differential equations of neutral type, the results obtained by Hale and Cooke for retarded equations and by Izé for neutral equations with constant lag. Haie considered a more general class of equations and was able to extend the results of Bellman and Cooke by proving that ∫∞ γ (t) dt < ∞ and μ is a simple characteristic root of x = L(xt) such that any other root with real part equal to Reμ is simple. A more general hypothesis can be used if one restricts to a particular subclass of C. The chapter presents subspace C of C of the continuous Lipschitz functions.
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