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.