Title :

Non-stability of Paneitz–Branson type equations in arbitrary dimensions

Author(s) :

Bakri, Laurent [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Casteras, Jean-Baptiste [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]

Journal title :

Nonlinear Analysis: Theory, Methods and Applications

Pages :

118-133

Publisher :

Elsevier

Publication date :

2014-09

ISSN :

0362-546X

English keyword(s) :

Paneitz-Branson type equations
Liapunov-Schmidt reduction procedure
blow up solutions

HAL domain(s) :

Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

Let $(M, g)$ be a compact riemannian manifold of dimension $n\geq 5$. We consider a Paneitz-Branson type equation with general coefficients $(E)\Delta_{g}^{2} u − div_g (A_g du) + hu = |u| \frac{2 * −2−\epsilon} u$ on $M$, ...
Show more >Let $(M, g)$ be a compact riemannian manifold of dimension $n\geq 5$. We consider a Paneitz-Branson type equation with general coefficients $(E)\Delta_{g}^{2} u − div_g (A_g du) + hu = |u| \frac{2 * −2−\epsilon} u$ on $M$, (E) where $A_g$ is a smooth symmetric (2, 0)-tensor, $h\in C^\infty (M), 2 * = \frac{2n}{n − 4}$ and $\epsilon$ is a small positive parameter. Assuming that there exists a positive nondegenerate solution of (E) when $\epsilon = 0$ and under suitable conditions, we construct solutions $u_\epsilon$ of type $(u_0 − BBl_\epsilon)$ to (E) which blow up at one point of the manifold when $\epsilon$ tends to 0 for all dimensions $n\geq 5$.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL