Given (M,g) a smooth, compact Riemannian n-manifold, we consider equations like \Delta_g u+hu = u^{2*-1-\eps} where \Delta_g is the laplace beltrami operator, h is a C^1 function on M, the exponent 2* = 2n/(n-2) is critical from the Sobolev viewpoint, and \eps is a small real parameter such that \eps -> 0. We prove the existence of blowing-up families of positive solutions in the subcritical and supercritical case when the graph of h is distinct at some point from the graph of (n-2)/(4n-4) Scal_g, Scal_g being the scalar curvature.

Blow up solutions for asimptotically critical elliptic equations on Riemannian manifolds

MICHELETTI, ANNA MARIA;
2009-01-01

Abstract

Given (M,g) a smooth, compact Riemannian n-manifold, we consider equations like \Delta_g u+hu = u^{2*-1-\eps} where \Delta_g is the laplace beltrami operator, h is a C^1 function on M, the exponent 2* = 2n/(n-2) is critical from the Sobolev viewpoint, and \eps is a small real parameter such that \eps -> 0. We prove the existence of blowing-up families of positive solutions in the subcritical and supercritical case when the graph of h is distinct at some point from the graph of (n-2)/(4n-4) Scal_g, Scal_g being the scalar curvature.
2009
Micheletti, ANNA MARIA; Pistoia, A; Vetois, J.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/132466
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