Prescribing Webster scalar curvature on CR manifolds of negative conformal invariants

In this paper, we are interested in solving the following partial differential equation − Δ θ u + R u = f u 1 + 2 / n on a compact strictly pseudo-convex CR manifold ( M , θ ) of dimension 2 n + 1 with n ⩾ 1 . This problem naturally arises when solving the prescribing Webster scalar curvature problem on M with the prescribed function f . Using variational techniques, we prove several non-existence, existence, and multiplicity results when the function f is sign-changing.