Blow-up solutions for Paneitz-Branson type equations with critical growth

摘要

Let (M, g) be a smooth, compact Riemannian manifold of dimension n≥7. We consider the Paneitz-Branson type equation △_g~2u - div_g(△du) + au = |u|~(2~#)-2-ε u in M,rnwhere △_g = - div _g ▽ is the Laplace-Beltrami operator, A is a smooth symmetrical (2,0)-tensor fields, a is a smooth function on M, 2~# = 2n-4 is the critical exponent for the Sobolev embedding and e is a small positive parameter. Under suitable conditions on the Tr_g A, we construct solutions u_ε which blow up at one point of the manifold as e goes to zero.