Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds

Given a smooth compact Riemannian n-manifold (M,g), we consider the equation Δgu+hu=|u|2⁎−2−εu, where h is a C1-function on M, the exponent 2⁎:=2n/(n−2) is the critical Sobolev exponent, and ε is a small positive real parameter such that ε→0. We prove the existence of blowing-up families of sign-changing solutions which develop bubble towers at some point where the function h is greater than the Yamabe potential .