Given (M,g) a smooth compact Riemannian N-manifold, we we show that positive solutions to the problem -\eps^2\Delta_gu + u = u^{p-1} in M, u > 0 in M are generated by stable critical points of the scalar curvature of g, provided \eps is small enough. Here \Delta_g is the laplace beltrami operator, \eps is a small real parameter and p > 2 if N = 2 and 2 < p < 2* = 2N/(N-)2 if N>2
The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds
MICHELETTI, ANNA MARIA;
2009-01-01
Abstract
Given (M,g) a smooth compact Riemannian N-manifold, we we show that positive solutions to the problem -\eps^2\Delta_gu + u = u^{p-1} in M, u > 0 in M are generated by stable critical points of the scalar curvature of g, provided \eps is small enough. Here \Delta_g is the laplace beltrami operator, \eps is a small real parameter and p > 2 if N = 2 and 2 < p < 2* = 2N/(N-)2 if N>2File in questo prodotto:
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