- Turkish Journal of Mathematics
- Vol: 42 Issue: 4
- A nonexistence result for blowing up sign-changing solutions of the Brezis-Nirenberg-type problem
A nonexistence result for blowing up sign-changing solutions of the Brezis-Nirenberg-type problem
Authors : Yessine Dammak
Pages : 1630-1654
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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