Blow-up solutions for linear perturbations of the Yamabe equation

For a smooth, compact Riemannian manifold (M,g) of dimension $N \geg 3$, we are interested in the critical equation $Δ_g u+(N-2/4(N-1) S_g+εh)u=u^{N+2/N-2} in M, u>0 in M,$ where Δ_g is the Laplace--Beltrami operator, S_g is the Scalar curvature of (M,g), $h\in C^{0,α}(M)$, and $ε$ is a small parameter.

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