We describe an alternative approach to the existence results of S.-Y. A. Chang and P. C. Yang for metrics of prescribed scalar curvature on via the prescribed curvature flow. Moreover, we give an example showing that the results of these authors in general cannot be improved upon.
"A flow approach to Nirenberg's problem." Duke Math. J. 128 (1) 19 - 64, 15 May 2005. https://doi.org/10.1215/S0012-7094-04-12812-X