ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35 Chen, Wenxiong Southwest Missouri State Univ. Springfield MO 65804; Chang, Sun-Yung University of California Los Angeles, CA 90095, USA High Order Conformally Invariant Equations We consider the existence and classification of solutions of higher order conformally invariant equation in R^{n}

(−Δ)^{\frac{n}{2}} u = (n − 1)!e^{nu}

with

∫_{R^{n}} e^{nu}dx < ∞.

Let α = \frac{2}{|S^{n}|} ∫ e^{nu}dx. We show that

(a) α ≤ 2;

(b) if α = 2, all the solutions are radially symmetric;

(c) for every 0 < α ≤ 2, there exists at least one solution.