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The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds. (English) Zbl 1161.58310

Let (M,g) be a smooth compact Riemannian N-manifold, N2, and p>2 if N=2 and 2<p<2 * =2N N-2 if N3· The authors show that the positive solutions of the problem

-ε 2 Δ g u+u=u p-1 inM

are generated by stable critical points of the scalar curvature of g, if ε is small enough.

MSC:
58J05Elliptic equations on manifolds, general theory
58E30Variational principles on infinite-dimensional spaces
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