On a planar Liouville-type problem in the study of selfgravitating strings

Motivated by the construction of selfgravitating strings (cf. Yang, 2001, 1994 [22,23]), we analyze a Liouville-type equation on the plane, derived in Yang (1994) [23]. We establish sharp existence and uniqueness properties for the corresponding radial solutions. We investigate also when the problem allows for non-radial solutions.