{
"id" : "n165454SE",
"class" : "Document",
"title" : "Radial symmetry of large solutions of nonlinear elliptic equations",
"abstract" : "
We give conditions under which all C2C^2 solutions of the problem amp;u=f(|x|,u),xRn,amp;lim|x|u(x)=\\begin{align*} &Delta u = f(|x|,u),qquad xin {mathbb {R}}^n, &lim _{|x|\to infty } u(x) = infty end{align*} are radial. We assume f(|x|,u)f(|x|,u) is positive when |x||x| and uu are both large and positive. Since this problem with f(|x|,u)=