Mousa Jaber Abu Elshour

Asymptotic Representations of the Solutions of a Class of the Second Order Nonautonomous Differential Equations

abstract:
For the second order nonlinear nonautonomous differential equation $$ y''=\alpha_0p(t)y|\ln|y||^\sigma, $$ 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 are established as $t\to +\infty$.

Mathematics Subject Classification: 34D05

Key words and phrases: Nonlinear differential equations, non-oscillatory solutions, asymptotic representations