Existence of nonoscillatory solutions of first order nonlinear neutral equations

TL;DRAbstract

Abstract Consider the nonlinear neutral equation where p i (t), h i (t), g j (t), Q(t) Є C[t 0 , ∞), lim t →∞ h i (t) = ∞, lim t →∞ g j (t) = ∞ i Є I m = {1, 2, …, m }, j Є I n = {1, 2, …, n }. We obtain a necessary and sufficient condition (2) for this equation to have a nonoscillatory solution x(t) with lim t →∞ inf| x(t) | > 0 (Theorems 5 and 6) or to have a bounded nonoscillatory solution x(t) with lim t →∞ inf| x(t) | > 0 (Theorem 7).

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