Further study of a weighted elliptic equation  

作　　者：GUO ZongMing WAN FangShu 

机构地区：[1]Department of Mathematics, Henan Normal University, Xinxiang 453007, China

出　　处：《Science China Mathematics》2017年第12期2391-2406,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 11571093)

摘　　要：A Liouville type result is established for non-negative entire solutions of a weighted elliptic equation.This provides a positive answer to a problem left open by Du and Guo(2015) and Phan and Souplet(2012)(see(CJ) by Du and Guo(2015) and Conjecture B by Phan and Souplet(2012)). Meanwhile, some regularity results are also obtained. The main results in this paper imply that the number ps is the critical value of the Dirichlet problems of the related equation, even though there are still some open problems left. Our results also apply for the equation with a Hardy potential.A Liouville type result is established for non-negative entire solutions of a weighted elliptic equation.This provides a positive answer to a problem left open by Du and Guo（2015） and Phan and Souplet（2012）（see（CJ） by Du and Guo（2015） and Conjecture B by Phan and Souplet（2012））. Meanwhile, some regularity results are also obtained. The main results in this paper imply that the number ps is the critical value of the Dirichlet problems of the related equation, even though there are still some open problems left. Our results also apply for the equation with a Hardy potential.

关 键 词：positive solutions EMBEDDINGS weighted elliptic equations critical values Liouville theorem 

分 类 号：O175.25[理学—数学]