Chen, Wenxiong; Ding, Weiyue Scalar curvatures on S 2. (English) Zbl 0635.35026 Trans. Am. Math. Soc. 303, 365-382 (1987). The authors prove a theorem for the existence of a solution of the nonlinear elliptic equation \(-\Delta u+2=R(x)\ell\) 4, \(u\in S\) 2 under some conditions on R(x) but not symmetry. This is the first existence result where R(x) is not symmetric. The proof of the existence uses a mass center analysis technique and a continuous flow in H 1(S 2) controlled by \(\nabla R\). Reviewer: C.F.Wang Cited in 1 ReviewCited in 40 Documents MSC: 35J60 Nonlinear elliptic equations 35J20 Variational methods for second-order elliptic equations 53C99 Global differential geometry Keywords:existence; mass center; flow PDF BibTeX XML Cite \textit{W. Chen} and \textit{W. Ding}, Trans. Am. Math. Soc. 303, 365--382 (1987; Zbl 0635.35026) Full Text: DOI OpenURL