In this work we consider the boundary blow-up problem $$ \left\{ \begin{ array}{ ll} \Delta u = f(u) & \hbox{ in } B\\ \ \ u=+\infty & \hbox{ on }\partial B \end{ array} \right. $$ where $B$ stands for the unit ball of $\mathbb{ R}^N$ and $f$ is a locally Lipschitz function which is positive for large values and verifies the Keller-Osserman condition. Under an additional hypothesis on the asymptotic behavior of $f$ we show that all solutions of the above problem are radially symmetric and radially increasing. Our condition is sharp enough to generalize several results in previous literature.
Categories: math.AP