The fourth order elliptic problem with exponential nonlinearity

Abstract We consider the entire solution of the semilinear biharmonic equation Δ 2 u = e u , in R N , N ≥ 1 . For N = 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 ≥ 13 .