Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774028 | Journal of Differential Equations | 2017 | 68 Pages |
Abstract
We study the problem(Iε){âÎuâμu|x|2=upâεuqin Ω,u>0in Ω,uâH01(Ω)â©Lq+1(Ω), where q>pâ¥2ââ1, ε>0, ΩâRN is a bounded domain with smooth boundary, 0âΩ, Nâ¥3 and 0<μ<μ¯:=(Nâ22)2. We completely classify the singularity of solution at 0 in the supercritical case. Using the transformation v=|x|νu, we reduce the problem (Iε) to (Jε)(Jε){âdiv(|x|â2νâv)=|x|â(p+1)νvpâε|x|â(q+1)νvqin Ω,v>0in Ω,vâH01(Ω,|x|â2ν)â©Lq+1(Ω,|x|â(q+1)ν), and then formulating a variational problem for (Jε), we establish the existence of a variational solution vε and characterize the asymptotic behavior of vε as εâ0 by variational arguments when p=2ââ1.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mousomi Bhakta, Sanjiban Santra,