Asymptotic representations of solutions of nonautonomous ordinary differential equations with regularly varying nonlinearities

We obtain asymptotic representations as t ↑ ω, ω ≤ + ∞, for all possible types of P _ω(Y ₀, λ ₀)-solutions (where Y ₀ is zero or ±∞ and −∞ ≤ λ₀ ≤ +∞) of nonlinear differential equations y ⁽ⁿ⁾ = α ₀ p(t)φ(y), where α ₀ ∈ {−1, 1}, p: a, ω→]0,+∞ is a continuous function, and φ is a continuous regularly varying function in a one-sided neighborhood of Y ₀.