Bahri-Coron type theorem for the scalar curvature problem on high dimensional spheres |
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Authors: | Mohamed Ben Ayed |
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Institution: | 1. D??partement de Math??matiques, Universit?? de Sfax, Facult?? des Sciences, Route Soukra, Sfax, Tunisia
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Abstract: | We consider the existence and multiplicity results for the prescribed scalar curvature problem on the standard spheres of high dimension n ?? 7. Given a C 2 positive function K, using the theory of critical points at infinity, we prove an existence result as Bahri-Coron theorem. Our case is a generalization of Li (J Differ Equ 120:319?C410, 1995). Indeed, here the function K is flat near some critical points as in Li (J Differ Equ 120:319?C410, 1995) and it can have some nondegenerate critical points with ?? K ?? 0. Furthermore, using some topological arguments, we prove another kind of result. |
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