Affiliations: Departamento de Ingenieria Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile. E-mail: [email protected] | Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, via Antonio Scarpa 16, 00161 Roma, Italy. E-mail: [email protected]
Abstract: Let (M,g) be a smooth, compact Riemannian manifold of dimension n≥7. We consider the Paneitz–Branson type equation Δg2u−divg(A du)+au=|u|2♯−2−εu in M, where Δg=−divg∇ is the Laplace–Beltrami operator, A is a smooth symmetrical (2,0)-tensor fields, a is a smooth function on M, 2♯=2n/(n−4) is the critical exponent for the Sobolev embedding and ε is a small positive parameter. Under suitable conditions on the TrgA, we construct solutions uε which blow up at one point of the manifold as ε goes to zero.
Keywords: Paneitz–Branson type equations, critical exponent, blow up solutions, Liapunov–Schmidt reduction procedure
