Publication details
Solutions of half-linear differential equations in the classes Gamma and Pi
| Authors | |
|---|---|
| Year of publication | 2016 |
| Type | Article in Periodical |
| Magazine / Source | Differential and Integral Equations |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | half-linear differential equation; positive solution; asymptotic formula; regular variation; class Gamma; class Pi |
| Description | 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 $\alpha=2$. |
| Related projects: |