Asymptotic behavior of positive solutions of the nonlinear differential equation t^2u''=u^n

Abstract

In this article we study properties of positive solutions of the ordinary differential equation $t^2u''=u^n$ for $1<n\in\mathbb{N}$, we obtain conditions for their blow-up in finite time, and some properties for global solutions. Equations containing more general nonlinear terms are also considered.

Keywords

• Nonlinear differential equation
• Emden-Fowler equation
• blow-up rate