我們將討論橢圓方程$Delta u+K(|x|)u^{p}=0 mbox{in} R^{n}$(其中p>1，n>2)正則徑向解的分類，已知此方程的任何徑向解必有零點或滿足快速遞降，或滿足緩慢遞降。在此論文中，我们將初值為alpha的解記做$u(r; alpha)$時，當$K(r)$滿足某些條件時，我們利用參數$r_{G}$跟$r_{H}$(被$K(r)$所決定)，將方程式的徑向解結構可以分成下列三型:
Z 型：對任意初值$alphain(0,infty)$時，u在$(0,infty)$ 上有零點。
S 型：u對任意初值$alphain(0,infty)$時，u在$(0,infty)$ 上的振幅便緩慢遞降。
M 型：存在一個初值$alpha_{f}$使得當初值$alphain(alpha_{f},infty)$時，u在$(0,infty)$ 上有零點。當初值$alpha=alpha_{f}$時，u在$(0,infty)$ 上的振幅便緩慢遞降。當初值$alphain(0,alpha_{f})$時，u在$(0,infty)$ 上的振幅便快速遞降。以上乃日本教授Yanagida和Yotsutani好幾篇論文的工作，我在此論文做一個整理報告。

In this thesis, we shall give a concise account for the classification of the structure of positive radial solutions of the semilinear elliptic equation$$Delta u+K(|x|)u^{p}=0 .$$ It is known that a radial solution $u$ is crossing if $u$ has a zero in $(0, infty)$; $u$
is slowly decaying if $u$ is positive but $displaystylelim_{r
ightarrow{infty}}r^{n-2}u=infty$; u is rapidly decaying if $u$ is positive,
$displaystylelim_{r
ightarrow{infty}}r^{n-2}u$ exists and is positive. Using some Pohozaev identities, we show that under certain condition on $K$, by comparing some parameters $r_{G}$ and $r_{H}$, the structure of positive radial solutions for various initial conditions can be classified as Type Z ($u(r; alpha)$ is crossing for all $r>0$ ), Type S ($u(r; alpha)$ is slowly decaying for all $r>0$), and Type M (there is some $alpha_{f}$ such that
$u(r; alpha)$ is crossing for $alphain(alpha_{f},
infty)$, $u(r; alpha)$ is slowly decaying for
$alpha=alpha_{f}$, and $u(r; alpha)$ is rapidly decaying for $alphain(0, alpha_{f})$). The above work is due to Yanagida and Yotsutani.

1.Introduction
2.Properties of solutions
3.Kelvin Transformation
4.Proof of Theorem A
5.Proof of Key Proposition

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