Nodal solutions for a Paneitz-Branson type equation

Abstract

Let (M,g) be a smooth compact Riemannian manifold of dimension n≥5. Denote Lg the Paneitz-Branson type operator. In this paper, we show that there exists a nodal solution (solution with changing sign) of the nonlinear Paneitz-Branson type equation Lgv=ϵ|v|N−2v where ϵ<0. At the end, we give a geometric application of the above equation.