Abstract
By using the equivalent integral form for the Q -curvature equation, we generalize the well-known non-existence results on two-dimensional Gaussian curvature equation to all dimensional Q -curvature equation. Somehow, we introduce a new approach to Q -curvature equation which is higher order and even pseudo-differential equation. As a by-product, we do classify the solutions for Q = 1 solutions on S n as well as on R n with necessary growth rate assumption.
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