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.
2009
Dancer, N; Micheletti, ANNA MARIA; Pistoia, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/131013
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