Electron. J. Diff. Equ., Vol. 2013 (2013), No. 250, pp. 1-9.

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

Meng-Rong Li, Hsin-Yu Yao, Yu-Tso Li

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.

Submitted October 5, 2013. Published November 20, 2013.
Math Subject Classifications: 34A34, 34C11, 34C60.
Key Words: Nonlinear differential equation; Emden-Fowler equation; blow-up rate.

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Meng-Rong Li
Department of Mathematical Sciences
National Chengchi University
Taipei, Taiwan
email: liwei@math.nccu.edu.tw
  Hsin-Yu Yao
Department of Mathematical Sciences
National Chengchi University
Taipei, Taiwan
email: diadia0914@gmail.com
  Yu-Tso Li
Department of Aerospace and Systems Engineering
Feng Chia University
Taichung, Taiwan
email: joycelion74@gmail.com

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