Non-degeneracy of the bubble solutions for the Henon equation and applications

We consider the following Henon equation with critical growth: {-Delta u = K(vertical bar y vertical bar)u(N+2/N-2), u > 0, in B-1(0) u = 0, on partial derivative B-1(0), where B-1(0) is the unit ball in R-N, K : [0, 1] -> R+ is a bounded function and K ''(1) exists. We prove a non-degeneracy result of the bubble solutions constructed in [24] via the local Pohozaev identities for N >= 5. Then, as applications, by using reduction arguments combined with delicate estimates for the modified Green function and the error, we prove the new existence of infinitely many non-radial solutions, whose energy can be arbitrarily large.