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

Advances in Nonlinear Analysis

Vitolo Antonio¹  Mohammed Ahmed²  Rădulescu Vicenţiu D.³ 

[1] and Faculty of Applied Mathematics, AGH University of Science and Technology, 30-059 Kraków, Poland;Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA;Institute of Mathematics, Physics and Mechanics, 1000Ljubljana, Slovenia;

关键词: large solutions;    existence and uniqueness;    fully nonlinear elliptic equations;    35j60;    35j70;   

DOI  :  10.1515/anona-2018-0134

来源: DOAJ

【 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,D2⁢u)=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}}. 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】

Unknown