Blow-up solutions for fully nonlinear equations: Existence, asymptotic estimates and uniqueness

The primary objective of the paper is to study the existence, asymptotic boundary estimates and uniqueness of large solutions to fully nonlinear equations H (x, u, Du, D2u) = f(u) + h(x) in bounded C2 domains Ω ⊆ Rn. Here H is a fully nonlinear uniformly elliptic differential operator, f is a non-decreasing function that satisfies appropriate growth conditions at infinity, and h is a continuous function on Ω that could be unbounded either from above or from below. The results contained herein provide substantial generalizations and improvements of results known in the literature.