article

Title: Blow-up solutions for asymptotically critical elliptic equations on Riemannian manifolds

Authors: Anna Maria Micheletti, Angela Pistoia and Jerome Vetois

Issue: Volume 58 (2009), Issue 4, 1719-1746

Abstract:

$Given $(M,g)$ a smooth, compact Riemannian $n$-manifold, we consider equations like $\varDelta_{g}u + hu = u^{2^{*}-1-\epsilon}$, where $h$ is a $C^{1}$-function on $M$, the exponent $2^{*} = 2n/(n-2)$ is critical from the Sobolev viewpoint, and $\epsilon$ is a small real parameter such that $\epsilon \to 0$. 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 $((n-2)/(4(n-1)))\mathrm{Scal}_{g}$.$