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

Advances in Nonlinear Analysis

article

Ahmed Mohammed¹  Vicenţiu D. Rădulescu²  Antonio Vitolo⁵ 

[1] Department of Mathematical Sciences, Ball State University;Institute of Mathematics;Faculty of Applied Mathematics, AGH University of Science and Technology;Institute of Mathematics “Simion Stoilow” of the Romanian Academy;Department of Civil Engineering

关键词: Large solutions;    existence and uniqueness;    fully nonlinear elliptic equations;   

DOI  :  10.1515/anona-2018-0134

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY