### Title page for etd-0809104-143110

URN etd-0809104-143110 Den-bon Chen m9024627@student.nsysu.edu.tw This thesis had been viewed 5217 times. Download 1515 times. Applied Mathematics 2003 2 Master English Classification of the Structure of Positive Radial Solutions to some Semilinear Elliptic Equation 2003-06-06 39 Semilinear Elliptic equation 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_{rightarrow{infty}}r^{n-2}u=infty\$; u is rapidly decaying if \$u\$ is positive,\$displaystylelim_{rightarrow{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. none - chair none - co-chair none - co-chair Chun-kong Law - advisor indicate access worldwide 2004-08-09

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