Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615188 | Journal of Mathematical Analysis and Applications | 2015 | 20 Pages |
Abstract
We studied the uniqueness of a nonnegative solution of the quasi-linear elliptic inequality(â)Îpu+uÏ⩽0 on a connected geodesically complete Riemannian manifold X, where Ï is a parameter and Îpu=div(|âu|pâ2âu). We proved that if p>1, Ï>pâ1, and for some x0âX,liminftâ0+tÏÏâp+1â«1âμ(B(x0,r))r(p+1)Ïâp+1Ïâp+1+pt2(pâ1)dr<â, then inequality (â) has no nontrivial nonnegative weak solutions. We also studied the weighed case and the sharpness of the main result.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jia-Cheng Huang,