Bubbling solutions for supercritical problems on manifolds
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Abstract
Let (M, g) be an n-dimensional compact Riemannian manifold without boundary and Gamma be a non-degenerate closed geodesic of (M, g). We prove that the supercritical problem
-Delta(g)u + hu = u(n+1/n+3) (+/-) (epsilon), u > 0, in (M, g)
has a solution that concentrates along Gamma as e goes to zero, provided the function h and the sectional curvatures along Gamma satisfy a suitable condition. A connection with the solution of a class of periodic Ordinary Differential Equations with singularity of attractive or repulsive type is established.
General note
Artículo de publicación ISI
Patrocinador
FONDECYT 1130360
Identifier
URI: https://repositorio.uchile.cl/handle/2250/132628
DOI: DOI:10.1016/j.matpur.2014.11.004
Quote Item
J. Math. Pures Appl. 103(2015)1410–1440
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