A dierential equation y $y'' = α_0p(t)φ(y)$, where $α_0 ∈ \{-1, 1 \}, p: [α, ω [→]0, +∞[ (-∞ < α < ω ≤ +∞)$ is a continuous function, $φ: [y_0, +∞[→]0, +∞[$ is a twice continuously differentiable function that in a certain sence close to power function, is under consideration. The question on asymptotics of unbounded solutions of the equation is studied.

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