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

A note on a class of higher order conformally covariant equations

Sun-Yung Alice Chang 1, and  Wenxiong Chen 2,

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.

Keywords: non-uniqueness, variational method., Higher order semilinear elliptic equations, conformally covariant equations.
Mathematics Subject Classification: 35J6.
Citation: Sun-Yung Alice Chang, Wenxiong Chen. A note on a class of higher order conformally covariant equations. Discrete & Continuous Dynamical Systems, 2001, 7 (2) : 275-281. doi: 10.3934/dcds.2001.7.275
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