V. M. Evtukhov and Mousa Jaber Abu Elshour

Asymptotic Behavior of Solutions of Second Order Nonlinear Differential Equations Close to Linear Equations

abstract:
The differential equation $$ y''=\alpha_0p(t)y|\ln|y||^\sigma, $$ is considered in a finite or infinite interval $[a,\omega[$, where $\alpha_0\in\{-1,1\}$, $\sigma\in \mathbb{R},$ and
$p:[a,\omega[\,\to\,]0,+\infty[$ is a continuous function. Asymptotic representations of solutions of this equation is obtained as $t\to \omega$.

Mathematics Subject Classification: 34E05

Key words and phrases: Nonlinear differential equations, nonoscillation solutions, asymptotic representations