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A note on a class of higher order conformally covariant equations
1. | Department of Mathematics, Princeton University and UCLA, United States |
2. | Department of Mathematics, Southwest Missouri State University, United States |
$(- \Delta )^{\frac{n}{2}} w = (n -1)! e^{n w} x \in R^n$
for all even dimensions n.
Let
$\alpha = \frac{1}{|S^n|} \int_{R^n} e^{n w} dx .$
We prove, for every $0 < \alpha < 1$, the existence of at least one solution. In particular, for $ n = 4$, we obtain the existence of radial solutions.
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