Title page for etd-0809104-143110


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URN etd-0809104-143110
Author Den-bon Chen
Author's Email Address m9024627@student.nsysu.edu.tw
Statistics This thesis had been viewed 5067 times. Download 1458 times.
Department Applied Mathematics
Year 2003
Semester 2
Degree Master
Type of Document
Language English
Title Classification of the Structure of Positive Radial Solutions to some Semilinear Elliptic Equation
Date of Defense 2003-06-06
Page Count 39
Keyword
  • Semilinear Elliptic equation
  • Abstract 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.
    Advisory Committee
  • none - chair
  • none - co-chair
  • none - co-chair
  • Chun-kong Law - advisor
  • Files
  • etd-0809104-143110.pdf
  • indicate access worldwide
    Date of Submission 2004-08-09

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