Singular periodic solutions to a critical equation in the Heisenberg group

We construct positive solutions to the equation-Delta(Hn)u = u(Q+2/Q-2)on the Heisenberg group, singular in the origin, similar to the Fowler solutions of the Yamabe equations on R-n. These satisfy the homogeneity property u o delta(T) = T-(Q-2)/2 u for some T large enough, where Q = 2n + 2 and delta(T) is the natural dilation in H-n. We use the Lyapunov-Schmidt method applied to a family of approximate solutions built by periodization from the global regular solution classified by Jerison and Lee (1988).