Existence of solutions for an approximation of the Paneitz problem on spheres

This paper is devoted to studying the nonlinear problem with subcritical exponent (Sε) : Δ²u-cₙΔ u+dₙu = Kun+4/n-4-ε, u on Sⁿ, where n≥5, ε is a small positive parameter and K is a a smooth positive function on Sⁿ. We construct some solutions which blow up at q different critical points of K.