| Contents |
| In the talk, we will consider the half-linear differential
equation $$(r(t)|y'|^{\alpha-2} y')'=p(t)|y|^{\alpha-2} y,$$ where
$r$ and $p$ are positive continuous functions on $[a,\infty)$ and
$\alpha\in(1,\infty)$. We will show how the Karamata theory of
regularly varying functions and the de Haan theory can be utilized
in the study of asymptotic behavior of positive solutions to the
half-linear equation. In particular, we will give conditions
guaranteeing that increasing solutions are in the de Haan class
$\Gamma$ and a similar type of statement will be obtained for
decreasing solutions. Further, we will deal with a description of
behavior of slowly varying solutions, where the theory of the de
Haan class $\Pi$ finds applications. We will also mention the
concept of nearly (half-)linear equations. |
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