# American Institute of Mathematical Sciences

April  2001, 7(2): 275-281. doi: 10.3934/dcds.2001.7.275

## 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

Revised  September 2000 Published  January 2001

In this paper, we study the higher order conformally covariant equation

$(- \Delta )^{\frac{n}{2}} w = (n -1)! e^{n w} x \in R^n$

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.

Citation: Sun-Yung Alice Chang, Wenxiong Chen. A note on a class of higher order conformally covariant equations. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 275-281. doi: 10.3934/dcds.2001.7.275
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