Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899137 | Journal of Differential Equations | 2017 | 29 Pages |
Abstract
We consider the following slightly subcritical problem(âε){âÎu=β(x)|u|pâ1âεuin Ω,u=0on âΩ, where Ω is a smooth bounded domain in Rn, 3â¤nâ¤6, p:=n+2nâ2 is the Sobolev critical exponent, ε is a small positive parameter and βâC2(Ωâ¾) is a positive function. We assume that there exists a nondegenerate critical point ξâââΩ of the restriction of β to the boundary âΩ such thatâ(β(ξâ)â2pâ1)â
η(ξâ)>0, where η denotes the inner normal unit vector on âΩ. Given any integer kâ¥1, we show that for ε>0 small enough problem (âε) has a positive solution, which is a sum of k bubbles which accumulate at ξâ as ε tends to zero. We also prove the existence of a sign changing solution whose shape resembles a sum of a positive bubble and a negative bubble near the point ξâ.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Juan Dávila, Jorge Faya, Fethi Mahmoudi,