## A note on a Liouville-type result for a system of fourth-order equations in $$\mathbb R^N$$.(English)Zbl 1068.35512

Summary: 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 bi-Laplacian 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.

### MSC:

 35J60 Nonlinear elliptic equations
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