Дослiджується питання про асимптотику необмежених розв'язкiв диференцiальних рiвнянь виду y $y'' = α_0p(t)φ(y)$, де $α_0 ∈ \{-1, 1 \}, p: [α, ω [→]0, +∞[ (-∞ < α < ω ≤ +∞)$ -  неперервна функцiя, а $φ: [y_0, +∞[→]0, +∞[$ - двiчi неперервно диференцiйовна функцiя, у деякому сенсi близька до степеневої.

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