  In this paper we consider second order fully nonlinear operators with an
additive superlinear gradient term. Like in the pioneering paper of Brezis for
the semilinear case, we obtain the existence of entire viscosity solutions,
defined in all the space, without assuming global bounds. A uniqueness result
is also obtained for special gradient terms, subject to a convexity/concavity
type assumption where superlinearity is essential and has to be handled in a
different way from the linear case.
