### Title page for etd-0616103-180709

URN etd-0616103-180709 Jiunn-Yean Shiao shiaujy@math.nsysu.edu.tw This thesis had been viewed 5178 times. Download 2144 times. Applied Mathematics 2002 2 Master English The Structure of Radial Solutions to a Semilinear Elliptic Equation and A Pohozaev Identity 2003-06-06 34 semilinear elliptic equation Pohozaev identity The elliptic equation \$Delta u+K(|x|)|u|^{p-1}u=0,xinmathbf{R}^{n}\$ is studied, where \$p>1\$, \$n>2\$, \$K(r)\$ issmooth and positive on \$(0,infty)\$, and \$rK(r)in L^{1}(0,1)\$. Itis known that the radial solution either oscillates infinitely, or\$lim_{rightarrowinfty}r^{n-2}u(r;al) in Rsetminus{0}\$ (rapidly decaying), or \$lim_{rightarrow infty}r^{n-2}u(r;al) = infty (or -infty)\$ (slowly decaying). Let \$u=u(r;al)\$ is a solutionsatisfying \$u(0)=al\$. In this thesis, we classify all theradial solutions into three types:Type R(\$i\$): \$u\$ has exactly \$i\$ zeros on \$(0,infty)\$, and israpidly decaying at \$r=infty\$.Type S(\$i\$): \$u\$ has exactly \$i\$ zeros on \$(0,infty)\$, and isslowly decaying at \$r=infty\$.Type O: \$u\$ has infinitely many zeros on \$(0,infty)\$.If \$rK_{r}(r)/K(r)\$ satisfies some conditions, then the structureof radial solutions is determined completely. In particular, thereexists \$0

Browse | Search All Available ETDs