Exponential Analysis of Solutions of Functional Differential Equations with Unbounded Terms

where x ∈ R, G : R × R → R is a given nonlinear continuous function in t and x. For a vector x ∈ R we take |x| to be the Euclidean norm of x. Let t0 ≥ 0, then for each continuous function φ : [0, t0] → R, there is at least one continuous function x(t) = x(t, t0, φ) on an interval [t0, I] satisfying (1.1) for t0 ≤ t ≤ I and such that x(t, t0, φ) = φ(t) for 0 ≤ t0 ≤ I. It is assumed that the right hand derivative, x′(t) of x(t) exist at t = t0. For conditions ensuring existence, uniqueness and continuability of solutions of (1.1) we refer the reader to [3] .