The higher order neutral functional differential equation (1) dn/dtn[x(t) + h(t)x(τ(t))] + σ f(t, x(g(t))) = 0 is considered under the following conditions: n ≥ 2, σ = ±1, τ(t) is strictly increasing in t ∈ [t0 ∞), τ(t) < t for t ≥ t0, limt→∞ τ(t) = ∞, limt→∞ g(t) = ∞, and f(t, u) is nonnegative on [t0, ∞) × (0, ∞) and nondecreasing in u ∈ (0, ∞). A necessary and sufficient condition is derived for the existence of certain positive solutions of (1).
- Neutral differential equation
- Positive solution
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