Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
841465 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 9 Pages |
Abstract
We prove the nonexistence of solutions for a prescribed mean curvature equation {−div(∇u1+|∇u|2)=λ|u|p−1u,x∈BR⊆Rn,u=0,x∈∂BR, when p⩾1p⩾1 and the positive parameter λλ is small. The result extends theorems of Narukawa and Suzuki, and Finn, from the case of n=2,p=1n=2,p=1 to all n⩾2,p⩾1n⩾2,p⩾1. Moreover, our proof is very simple and the result is not limited to positive (and negative) solutions. We also show that a similar result for positive solutions is still true if |u|p−1u|u|p−1u is replaced by the exponential nonlinearity eu−1eu−1.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Hongjing Pan, Ruixiang Xing,