A subcritical approximation of the Paneitz problem on spheres

This paper is concerned with the following subcritical approximation of a fourth order conformal invariant (the Paneitz curvature) on spheres ( S ε ) : Δ 2 u - c n Δ u + d n u = K | u | 8 n - 4 - ε u , in S n , where n ≥ 5 , ε is a small positive parameter and K is a smooth positive function on S n . We construct some sign-changing solutions which blow up at two different critical points of K . Furthermore, we construct sign-changing solutions of ( S ε ) having two bubbles and blowing up at the same critical point of K .