The $Q$-curvature on a 4-dimensional Riemannian manifold $(M,g)$ with   $\int_MQdV_g=8\pi^2$
  In this paper we study the solutions of the $Q$-curvature equation on a 4-dimensional Riemannian manifold $(M,g)$ with $\int_MQdV_g=8\pi^2$, proving some sufficient conditions for the existence. 
Jiayu Li, Yuxiang Li, Pan Liu