A nonexistence result for blowing up sign-changing solutions of the Brezis-Nirenberg-type problem

Authors : Yessine DAMMAK

Pages : 1630-1654

View : 10 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

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 $\mathbb{R}^n$, $n\geq4$, $p+1=2n/insert ignore into journalissuearticles values(n-2);$ 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 $insert ignore into journalissuearticles values(P_{-\varepsilon});$ with two positive and one negative blow up points.
Keywords : Blow up analysis, sign changing solutions, lack of compactness, critical exponent