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

作者：Bakri Laurent; Casteras Jean Baptiste^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2014, 107: 118-133.

DOI：10.1016/j.na.2014.05.006

• Paneitz-Branson type equations
• Blow up solutions
• Lyapunov-Schmidt reduction procedure

Let (M, g) be a compact riemannian manifold of dimension n >= 5. We consider a Paneitz-Branson type equation with general coefficients
Delta(2)(g)u - div(g)(A(g)du) + hu = vertical bar u vertical bar(2)*(-2-epsilon)u on M,
where A(g) is a smooth symmetric (2, 0)-tensor, h is an element of C-infinity(M), 2* = 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) - BBI epsilon) to (E) which blow up at one point of the manifold when epsilon tends to 0 for all dimensions n >= 5.

• 出版日期2014-9