Classification of Positive Solutions to a Divergent Equation on the Upper Half Space

• 作者: Jin Ge YAO Jing Bo DOU
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（3）
• 页码范围: 499-509
• 页数: 11页
• 语种: 英文

摘要

In this paper we classify the positive solutions of the divergent equation with Neumann boundary on the upper half space{-div(tα▽u) =tβf(u),(y,t) ∈ Rn+1+,limt→0+ tα(e)u/(e)t =0 by the method of moving spheres and Kelvin transformations,where n ≥ 1,α ＞ 0,β ＞-1,n-1/n+1β ≤α ＜ β + 2,and f :(0,∞) → (0,o∞) is non-negative continuous function satisfying some conditions.This equation arises from a weighed Sobolev inequality involving divergent operator div(tα▽u) on the upper half space.