Given (M, g) a smooth compact Riemannian N-manifold, we prove that for any fixed positive integer K the problem −ε2gu + u = u p−1 in M, u > 0 in M has a K-peaks solution, whose peaks collapse, as ε goes to zero, to an isolated local minimum point of the scalar curvature. Here p > 2 if N = 2 and 2 < p < 2∗ = 2N/N−2 if N ≥ 3.
Multipeak solutions for some singularly perturbed nonlinear elliptic problems on riemannian manifolds / E. N., Dancer; A. M., Micheletti; Pistoia, Angela. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - STAMPA. - 128:2(2009), pp. 163-193. [10.1007/s00229-008-0225-4]
Multipeak solutions for some singularly perturbed nonlinear elliptic problems on riemannian manifolds
PISTOIA, Angela
2009
Abstract
Given (M, g) a smooth compact Riemannian N-manifold, we prove that for any fixed positive integer K the problem −ε2gu + u = u p−1 in M, u > 0 in M has a K-peaks solution, whose peaks collapse, as ε goes to zero, to an isolated local minimum point of the scalar curvature. Here p > 2 if N = 2 and 2 < p < 2∗ = 2N/N−2 if N ≥ 3.File allegati a questo prodotto
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
