Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations
Accurate asymptotic formulas for regularly varying solutions of the second order half-linear differential equation \begin{equation*} (|x'|^{\alpha}\textrm{sgn}\; x')' + q(t)|x|^{\alpha}\textrm{sgn}\; x = 0, \end{equation*} will be established explicitly, depending on the rate of deca...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2016-08-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4566 |
| Summary: | Accurate asymptotic formulas for regularly varying solutions of the second order half-linear differential equation
\begin{equation*}
(|x'|^{\alpha}\textrm{sgn}\; x')' + q(t)|x|^{\alpha}\textrm{sgn}\; x = 0,
\end{equation*}
will be established explicitly, depending on the rate of decay toward zero of the function
\begin{equation*}Q_c(t) = t^{\alpha}\int_t^{\infty}q(s)ds - c\end{equation*}
as $t\to\infty$, where $c<\alpha^\alpha(\alpha+1)^{-\alpha-1}$. |
|---|---|
| ISSN: | 1417-3875 |