Abstract
We study asymptotic behavior of (all) positive solutions of the non\-oscillatory half-linear differential equation of the form $$ (r(t)|y'|^ {\alpha-1}\text{sgn}\, y')'=p(t)|y|^{\alpha-1}\text{sgn}\, y , $$ 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 $\alpha=2$.
Citation
Valentina Taddei. Pavel Řehák. "Solutions of half-linear differential equations in the classes Gamma and Pi." Differential Integral Equations 29 (7/8) 683 - 714, July/August 2016. https://doi.org/10.57262/die/1462298681
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