Solutions of half-linear differential equations in the classes Gamma and Pi
| Autoři | |
|---|---|
| Rok publikování | 2016 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Differential and Integral Equations |
| Fakulta / Pracoviště MU | |
| Citace | |
| Obor | Obecná matematika |
| Klíčová slova | half-linear differential equation; positive solution; asymptotic formula; regular variation; class Gamma; class Pi |
| Popis | We study asymptotic behavior of (all) positive solutions of the non\-oscillatory half-linear differential equation of the form $(r(t)|y'|^ {\alpha-1}\sgn y')'=p(t)|y|^{\alpha-1}\sgn y$, where $\alpha\in(1,\infty)$ and $r,p$ are positive continuous functions on $[a,\infty)$, with the help of the Karamata theory of regularly varying functions and the de Haan theory. We show that increasing resp. decreasing solutions belong to the de Haan class $\Gamma$ resp. $\Gamma_-$ under suitable assumptions. Further we study behavior of slowly varying solutions for which asymptotic formulas are established. Some of our results are new even in the linear case $\alpha=2$. |
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