On the Generalized Emden–Fowler Equation

Abstract

This report contains a survey on recent results concerning solutions of the second order nonlinear differential equation $x'' + a(t)|x|^\gamma \operatorname{sgn} x = 0$, $\gamma > 0$, where $a(t)$ is continuous and nonnegative. Specifically, the questions concerning continuability, boundedness, stability, oscillation, asymptotic growth and boundary value problems are discussed. An extensive list of related references is also included.