Radial singular solutions for a fourth order equation with negative exponents

In this paper, we consider the radial singular solution ofΔ2u=−1up,inRNwithu>0,p>0. By using some elementary ordinary differential equation arguments, we prove the above equation admits no radial singular solution for N=3,p≥3. In addition, the exact asymptotic behaviors of the radial singular solution as r→0 is established for p=1,N≥4, which have a significant difference with the explicit singular solution. As a product, the singularity of any radial singular solution is of type II if p=1,N≥4.