Liouville-type results for semilinear elliptic equations in unbounded domains

摘要

This paper is devoted to the study of some class of semilinear elliptic equations in the whole space: $$ -a_{ij}(x)partial_{ij}u(x) -- q_i(x)partial_iu(x)=f(x,u(x)),quad xin{mathbb R}^N. $$ The aim is to prove uniqueness of positive- bounded solutions—Liouville-type theorems. Along the way, we establish also various existence results.