Blowing-up solutions concentrating along minimal submanifolds for some supercritical elliptic problems on Riemannian manifolds

Let $(M,g)$ and $(K,κ)$ be two Riemannian manifolds of dimensions $m$ and $k ,$ respectively. Let $ω\in C^2(N),$ $ω> 0.$ The warped product $M\times _ωK$ is the $(m+k)$-dimensional product manifold $M\times K$ furnished with metric $g+ω^2 κ.$ We prove that the supercritical problem $-Δ_{g+ω^2 κ}u+h u=u^{ {m+2\over m-2} \pm\varepsilon},\ u>0,\ \hbox{in}\ (M\times _ωK,g+ω^2 κ)$ has a solution which concentrate along a $k$-dimensional minimal submanifold $Γ$ of $M\times _ωN$ as the real parameter $\varepsilon$ goes to zero, provided the function $h$ and the sectional curvatures along $Γ$ satisfy a suitable condition.

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