Abstract
Let (Sn,g0) be the standard n-sphere. In this paper, we construct a sequence of conformal metricswith a given R ad their scalar curvature such that the energy of uj blows up as. We also construct sequence of gj with the given scalar curvature assuch that uj has a simultaneous concentraction of a given number of “bubbles” with the same concentraction centers. These examples show us that the blowing up behavior fo uj might be very complicated when the prescribled scalar curvature is a small perturbation of a positive constant.
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