Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904541 | Acta Mathematica Scientia | 2017 | 16 Pages |
Abstract
In this article, we consider the fractional Laplacian equation
{(âÎ)α/2u=K(x)f(u),xââ+n,uâ¡0,xââ+n,where
0<α<2,â+n:={x=(x1,x2,â¯,xn)|xn>0}. When K is strictly decreasing with respect to |xâ²|, the symmetry of positive solutions is proved, where xâ²=(x1,x2,ÄÄÄ,xnâ1) â
ânâ1. When K is strictly increasing with respect to xn or only depend on xn, the nonexistence of positive solutions is obtained.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Yanyan GUO,