Radial symmetry of large solutions of nonlinear elliptic equations Academic Article

We give conditions under which all C 2 C^2 solutions of the problem a m p ; u = f ( | x | , u ) , x R n , a m p ; lim | x | u ( x ) = \begin{align*} &Delta u = f(|x|,u),qquad xin {mathbb {R}}^n, &lim _{|x| o infty } u(x) = infty end{align*} are radial. We assume f ( | x | , u ) f(|x|,u) is positive when | x | |x| and u u are both large and positive. Since this problem with f ( | x | , u ) =