The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds

Micheletti, Anna; Pistoia, Angela
February 2009
Calculus of Variations & Partial Differential Equations;Feb2009, Vol. 34 Issue 2, p233
Academic Journal
Given ( M, g) a smooth compact Riemannian N-manifold, N = 2, we show that positive solutions to the problem are generated by stable critical points of the scalar curvature of g, provided $${\varepsilon}$$ is small enough. Here p > 2 if N = 2 and $${2 < p < 2^{*} = {2N \over N-2}}$$ if N = 3.


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