Blow-up solutions for linear perturbations of the Yamabe equation

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