Turkish Journal of Mathematics
DOI
10.3906/mat-1709-47
Abstract
We consider the Brezis-Nirenberg problem: $ -\triangle u= u ^{p-1}u\pm\varepsilon u\mbox{ in }\Omega;, \mbox{ with } u=0 \mbox{ on }\partial\Omega,$ where $\Omega$ is a smooth bounded domain in $\mathbb{R}^n$, $n\geq4$, $p+1=2n/(n-2)$ is the critical Sobolev exponent, and $\varepsilon > 0$ is a positive parameter. The main result of this paper shows that if $n\geq4$ there are no sign-changing solutions $u_\varepsilon$ of $(P_{-\varepsilon})$ with two positive and one negative blow up points.
Keywords
Blow-up analysis, sign-changing solutions, lack of compactness, critical exponent
First Page
1630
Last Page
1654
Recommended Citation
DAMMAK, YESSINE
(2018)
"A nonexistence result for blowing up sign-changing solutions of the Brezis-Nirenberg-type problem,"
Turkish Journal of Mathematics: Vol. 42:
No.
4, Article 7.
https://doi.org/10.3906/mat-1709-47
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss4/7
