Given (M,g) a smooth compact Riemannian N-manifold, we prove that for any fixed positive integer K the problem -\eps^2\Delta_gu + u = u^{p-1} in M, u > 0 in M has a K-peaks solution, whose peaks collapse, as \eps goes to zero, to an isolated local minimum point of the scalar curvature. 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.
Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian manifolds
MICHELETTI, ANNA MARIA;
2009-01-01
Abstract
Given (M,g) a smooth compact Riemannian N-manifold, we prove that for any fixed positive integer K the problem -\eps^2\Delta_gu + u = u^{p-1} in M, u > 0 in M has a K-peaks solution, whose peaks collapse, as \eps goes to zero, to an isolated local minimum point of the scalar curvature. 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.File in questo prodotto:
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