Bounded positive solutions of rotationally symmetric harmonic map equations

Abstract

We consider bounded positive solutions $\alpha$ of rotationally symmetric harmonic map equations. We study the continuity of the maps $\alpha' (0) \mapsto \alpha (\infty)$ and $\alpha (1) \mapsto \alpha (\infty)$ in connection with the Dirichlet problem at infinity. Regularity at zero, local properties and conditions for positive solutions to be blowing up, unbounded, or bounded are discussed.