The fourth order elliptic problem with exponential nonlinearity

We consider the entire solution of the semilinear biharmonic equation Δ2u=eu,inRN,N≥1. For N=3N=3, we obtain the asymptotic of the entire nonradial solution which extends the results of Lai and Ye (in press). Besides, a new singular solution of the above equation is constructed by derivative estimates for N≥13N≥13.