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

Abstract

Abstract 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 , D ⁢ u , D 2 ⁢ u ) = f ⁢ ( u ) + h ⁢ ( x ) {H(x,u,Du,D^{2}u)=f(u)+h(x)} in bounded C 2 {C^{2}} domains Ω ⊆ ℝ n {\Omega\subseteq\mathbb{R}^{n}} . 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.