Given (M, g) a smooth compact Riemannian N-manifold, N ≥ 2, we show that positive solutions to the problem -ε2Δgu + u = up-1 in M, are generated by stable critical points of the scalar curvature of g, provided ε is small enough. Here p > 2 if N = 2 and 2 < p < 2* = 2N/N-2 if N ≥ 3. © 2008 Springer-Verlag.
The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds / Anna Maria, Micheletti; Pistoia, Angela. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 34:2(2009), pp. 233-265. [10.1007/s00526-008-0183-4]
The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds
PISTOIA, Angela
2009
Abstract
Given (M, g) a smooth compact Riemannian N-manifold, N ≥ 2, we show that positive solutions to the problem -ε2Δgu + u = up-1 in M, are generated by stable critical points of the scalar curvature of g, provided ε is small enough. Here p > 2 if N = 2 and 2 < p < 2* = 2N/N-2 if N ≥ 3. © 2008 Springer-Verlag.File allegati a questo prodotto
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