Journal of Applied Mathematics
Volume 2012 (2012), Article ID 930868, 11 pages
http://dx.doi.org/10.1155/2012/930868
Research Article

A Problem Concerning Yamabe-Type Operators of Negative Admissible Metrics

Jin Liang1 and Huan Zhu2

1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China

Received 14 February 2012; Accepted 29 February 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Jin Liang and Huan Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is about a problem concerning nonlinear Yamabe-type operators of negative admissible metrics. We first give a result on 𝜎 𝑘 Yamabe problem of negative admissible metrics by virtue of the degree theory in nonlinear functional analysis and the maximum principle and then establish an existence and uniqueness theorem for the solutions to the problem.