Geodesic
Sign-changing solutions of a fourth-order elliptic equation with supercritical exponent
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article we study the nonlinear elliptic problem involving nearly critical exponent $$\displaylines{ \Delta^2 u = |u|^{8/(n-4)+\varepsilon}u\quad{in } \Omega, \cr \Delta u=u = 0\quad {on } \partial \Omega, }$$ where $\Omega $ is a smooth bounded domain in $\mathbb{R}^n $ with $n \geq 5 $, and $\varepsilon$ is a positive parameter. We show that, for $\varepsilon$ small, there is no sign-changing solution with low energy which blow up at exactly two points. Moreover, we prove that this problem has no bubble-tower sign-changing solutions.
Classification : 35J20, 35J60
Keywords: sign-changing solutions, critical exponent, bubble-tower solution 
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     author = {Bouh, Kamal Ould},
     title = {Sign-changing solutions of a fourth-order elliptic equation with supercritical exponent},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a8/}
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Bouh, Kamal Ould. Sign-changing solutions of a fourth-order elliptic equation with supercritical exponent. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a8/