Bubbling solutions for supercritical problems on manifolds

Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold without boundary and $Γ$ be a non degenerate closed geodesic of $(M,g)$. We prove that the supercritical problem $-Δ_gu+h u=u^{\frac{n+1}{n-3}\pmε},\ u>0,\ \hbox{in}\ (M,g)$ has a solution that concentrates along $Γ$ as $ε$ goes to zero, provided the function $h$ and the sectional curvatures along $Γ$ satisfy a suitable condition. A connection with the solution of a class of periodic O.D.E.'s with singularity of attractive or repulsive type is established.

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