$$-\Delta)^n u = K(x)e^{2nu},$$

on $\R^{2n}$, where $n \geq 1$ and $K \not\equiv 0$. We are interested in solutions with logarithmic growth at infinity. Mainly we will discuss the non-positive curvature case. In particular we give a more general condition for the existence of solutions for Gaussian curvature equation and we construct new type solutions with different remainder term at infinity. This is based on joint works with H.Y.Chen, X.Huang and D.Ye.