Existence of Nonoscillatory Solutions of First-Order Neutral Differential Equations

and Applied Analysis 3 We now define two maps S1 and S2 : Ω → C t0,∞ , R as follows: S1x t ⎧⎨ ⎩ a t x t − τ , t ≥ t1, S1x t1 , t0 ≤ t ≤ t1,