Blow-up solutions for linear perturbations of the Yamabe equation

Abstract

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