POSITIVE BLOW-UP SOLUTIONS FOR A LINEARLY PERTURBED BOUNDARY YAMABE PROBLEM

We consider the problem of prescribing the scalar and boundary mean curvatures via conformal deformation of the metric on a dimensional compact Riemannian manifold. We deal with the case of negative scalar curvature and boundary mean curvature of arbitrary sign which are non-constant and at some point of the boundary. It is known that this problem admits a positive mountain pass solution if , while no existence results are known for . We will consider a perturbation of the geometric problem and show the existence of a positive solution which blows-up at a boundary point which is critical for both prescribed curvatures.