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| Let $p$, $q$, $\phi $ be positive, continuous functions on a half-axis $[a,\infty )$. In the recent years a
number of papers appeared dealing with the asymptotic behavior for $t\rightarrow \infty $ of positive monotone
solutions $x(t)$ of the mentioned equation in the framework of regular variation in the sense of Karamata.
We present the precise asymptotic for $t\rightarrow \infty $ of increasing solutions for the cases
$$
\mbox{a)} \quad \phi (x) = x^{\gamma } , \; \gamma > 1 , \qquad \mbox{b)} \quad p(t) = 1 .
$$
Some of these result overlap with the ones of V.M. Evtukhov and A.M. Samoilenko for the $n$-th order
equation $x^{(n)} = q(t)\phi (x)$ studied by a different approach. |
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