A classification of solutions of a conformally invariant fourth order equation in

  • C.-S. Lin

    National Chung Cheng University, Chia-Yi, Taiwan

Abstract

In this paper, we consider the following conformally invariant equations of fourth order

and

where denotes the biharmonic operator in . By employing the method of moving planes, we are able to prove that all positive solutions of (2) are arised from the smooth conformal metrics on by the stereograph projection. For equation (1), we prove a necessary and sufficient condition for solutions obtained from the smooth conformal metrics on .

Cite this article

C.-S. Lin, A classification of solutions of a conformally invariant fourth order equation in . Comment. Math. Helv. 73 (1998), no. 2, pp. 206–231

DOI 10.1007/S000140050052