回顧一個重要的非線性二階方程式
d/dt(t^p(du/dt))+(-)t^(sigma)u^n=0,
這個方程式有許多有趣的物理應用，以Emden方程式的形式發生在天體物理學中；也以Fermi-Thomas方程式的形式出現在原子物理內。對於此類型的非線性方程式可以用來更頻繁且深入的探討數學物理，雖然目前仍存在著些許不確定性，不過如果在未來能有更全面的了解，這將有助於用來決定物理解的性質。
在這篇論文當中，我們討論微分方程式
t^2u"=u^p，p屬於N-{1},
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
d/dt(t^p(du/dt))+(-)t^(sigma)u^n=0,
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.
| Identifer | oai:union.ndltd.org:CHENGCHI/G0095751013 |
| Creators | 姚信宇 |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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