Prescribing Webster scalar curvature on CR manifolds of negative conformal invariants

In this paper, we are interested in solving the following partial differential equation−Δθu+Ru=fu1+2/n on a compact strictly pseudo-convex CR manifold (M,θ) of dimension 2n+1 with n⩾1. This problem naturally arises when solving the prescribing Webster scalar curvature problem on M with the prescribe...

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Bibliographic Details
Published in:Journal of Differential Equations 2015-06, Vol.258 (12), p.4443-4490
Main Authors: Ngô, Quốc Anh, Zhang, Hong
Format: Article
Language:English
Subjects:
Compact CR manifolds
Critical exponent
Negative conformal invariant
Prescribed Webster scalar curvature
Variational methods
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Summary:In this paper, we are interested in solving the following partial differential equation−Δθu+Ru=fu1+2/n on a compact strictly pseudo-convex CR manifold (M,θ) of dimension 2n+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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2015.01.040