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

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• 作者：Laurent Bakri^a ; ^{laurent.bakri@gmail.com" class="auth_mail} ; Jean-Baptiste Casteras^b ; ^{Jean-Baptiste.Casteras@univ-brest.fr" class="auth_mail}
• 关键词：35J30 ; 35J60 ; 35B33 ; 35B35
• 刊名：Nonlinear Analysis
• 出版年：September 2014
• 年：2014
• 卷：107
• 期：Complete
• 页码：118-133
• 全文大小：456 K

文摘

Let (M,g)$(M,g)$ be a compact riemannian manifold of dimension n≥5$n\ge 5$. We consider a Paneitz–Branson type equation with general coefficients where A_g$A_g$ is a smooth symmetric (2,0)$(2,0)$-tensor, h∈C^∞(M)$h\in C^{\infty }\left(M\right)$, $2^{\ast }=\frac{2n}{n-4}$ and 24934f21ac9f5" title="Click to view the MathML source">蔚$蔚$ is a small positive parameter. Assuming that there exists a positive nondegenerate solution of (E) when 蔚=0$蔚=0$ and under suitable conditions, we construct solutions u_蔚$u_{蔚}$ of type (u₀−BBl_蔚)$(u_0-BB{l}_{蔚})$ to (E) which blow up at one point of the manifold when 蔚$蔚$ tends to 0$0$ for all dimensions n≥5$n\ge 5$.