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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0809104-143110 |
| Date | 09 August 2004 |
| Creators | Chen, Den-bon |
| Contributors | none, none, none, Chun-kong Law |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0809104-143110 |
| Rights | unrestricted, Copyright information available at source archive |
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