Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 99, pp. 1-20.

Title: A note on a Liouville-type result for a system of fourth-order
  equations in R^N

Authors: Ana Rute Domingos (Univ. de Lisboa, Portugal)
         Yuxia Guo (Tsinghua Univ., Beijing, China)
         
Abstract: 
 We consider the fourth order system
 $\Delta^2 u =v^\alpha,\Delta^2 v =u^\beta$
 in  $\mathbb{R}^N$, for $N\geq 5$, with $\alpha\geq 1$,
 $\beta\geq 1$, where $\Delta^2$ is the bilaplacian operator.
 For $1/(\alpha +1) +1/(\beta +1)>(N-4)/N$ we prove the
 non-existence of non-negative, radial, smooth solutions.
 For  $\alpha,\beta\leq (N+4)/(N-4)$ we show the non-existence
 of non-negative smooth solutions.
   
Submitted November 27, 2001. Published November 27, 2002.
Math Subject Classifications: 35J60.
Key Words: Elliptic system of fourth order equations; moving-planes.