Existence of Nonoscillation Solutions of Higher-Order Nonlinear Neutral Differential Equations

In this paper, we consider the following higher-order nonlinear neutral differential equations: dn dtn [x(t) + cx(t - τ)] + (-1)n+1[P(t)f1 (x(t - σ)) - Q(t)f2 (x(t - δ))] = 0; t ≥ t0 where τ; σ; δ ∈ R+, c ∈ R; c ̸= ±1, and P(t); Q(t) ∈ C([t0; ∞); R+), fi(u) ∈ C(R; R), ufi(u) > 0. we obtain the results which are some sufficient conditions for existence of nonoscillation solutions, special case of the equation has also been studied.