Blow-up solutions for fully nonlinear equations: Existence, asymptotic estimates and uniqueness
Ahmed Mustefa Mohammed, Vicenţiu D. Rădulescu, Antonio Vitolo · Advances in Nonlinear Analysis · 2018
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,Du,D2u)=f(u)+h(x) {H(x,u,Du,D^{2}u)=f(u)+h(x)} in bounded C2 {C^{2}} domains Ω⊆ℝn {\Omega\subseteq\mathbb{R}^{n}} . HereHis a fully nonlinear uniformly elliptic differential operator,fis a non-decreasing function that satisfies appropriate growth conditions at infinity, andhis 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.