Given a smooth positive function $K$ on the standard sphere $(\\mathbb{S}^n,g_0)$, we use refined blow up analysis, Morse theoretical methods and counting index formulae to prove that, under generic conditions on the function $K$, there are arbitrarily many metrics $g$ conformally equivalent to $g_0$ and whose scalar curvature is given by the function $K$ provided that the function is sufficiently close to the scalar curvature of $g_0$. To prove such a multiplicity result we performed a refined blow up analysis of finite energy approximated solutions with non zero weak limit.<\/p>\n\n\n\n
This a joint work with M. Ben Ayed (Sfax University) and K. El Mehdi (Nouakchott University)<\/p>\n","protected":false},"excerpt":{"rendered":"
Given a smooth positive function $K$ on the standard sphere $(\\mathbb{S}^n,g_0)$, we use refined blow up analysis, Morse theoretical methods…<\/p>\n