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Title: 非線性微分方程式 t^2u";=u^p
On the nonlinear differential equation t^2u";=u^p
Authors: 姚信宇
Contributors: 李明融

Keywords: 正解的爆炸時間
blow-up time for positive solution
the life-span for positive solution
Emden-Fowler equation
Date: 2011
Issue Date: 2012-10-30 11:07:20 (UTC+8)
Abstract: 回顧一個重要的非線性二階方程式
其正解的性質。這個方程式是著名的 Emden-Fowler 方程式的一種特殊情形, 我們可以得到其解的一些有趣的現象及結果。
Recall the important nonlinear second-order equation
this equation has several interesting physical applications, occurring in astrophysics in the form of the Emden equation and in atomic physics in the form of the Fermi-Thomas equation. These seems a little doubt that nonlinear equations of this type would enter with greater frequency into mathematical physics, were it more widely known with what ease the properties of the physical solutions can be determined.
In this paper we discuss the property of positive solution of the ordinary differential equation
t^2u"=u^p, p belongs to N-{1},
this equation is a special case of the well-known Emden-Fowler equation, we obtain some interesting phenomena and resulits for solutions.
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