Boundary blow-up problems for Hessian equations

This paper is concerned with large solutions of Hessian equations $S_k(D^2u)=g(x,u)$ in a strictly k-convex domain, i.e. solutions that blow-up on the boundary of the domain. We prove existence, in the viscosity sense, of this kind of solutions assuming that g satisfies some natural growth conditions. Non-existence and uniqueness results are given too.