The asymptotic behavior of nonoscillatory solutions of the equation x + a ( t ) | x | γ sgn ⁡ x = 0 , γ > 0 x + a\left ( t \right ){\left | x \right |^\gamma }\operatorname {sgn} x = 0,\gamma > 0 , is discussed under the condition that A ( t ) = li m T → ∞ ∫ t T a ( s ) d s A\left ( t \right ) = {\text {li}}{{\text {m}}_{T \to \infty }}\int _t^T {a\left ( s \right )ds} exists and A ( t ) ≥ 0 A\left ( t \right ) \geq 0 for all t t . For the sublinear case of 0 > γ > 1 0 > \gamma > 1 , the existence of at least one nonoscillatory solution is completely characterized.