Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4619129 | Journal of Mathematical Analysis and Applications | 2010 | 14 Pages |
Abstract
We study positive solutions of the equationΔu=u−p−1in Ω⊂RN(N⩾2), where p>0p>0 and Ω is a bounded or unbounded domain. We show that there is a number pc=pc(N)⩾0pc=pc(N)⩾0 such that this equation with Ω=RNΩ=RN has no stable positive solution for p>pcp>pc. We further show that there is a critical power pc=pc(N)pc=pc(N) such that if p>pcp>pc, this equation with Ω=Br\{0}Ω=Br\{0} has no positive solution with finite Morse index that has an isolated rupture at 0; if 0
max{pc,pc}p>max{pc,pc}.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Zongming Guo, Li Ma,