A note on a Liouville-type result for a system of fourth-order equations in RN
Domingos, Ana Rute
Southwest Texas State University, Department of Mathematics
We consider the fourth order system Δ2u = vα, Δ2v = uβ in ℝN, for N ≥ 5, with α ≥ 1, β ≥ 1, where Δ2 is the bilaplacian operator. For 1/(α + 1) + 1 / (β + 1) > (N - 4) / N we prove the non-existence of non-negative, radial, smooth solutions. For α, β ≤ (N + 4) / (N - 4) we show the non-existence of non-negative smooth solutions.
Elliptic system of fourth order equations, Moving-planes
Domingos, A. R., & Guo, Y. (2002). A note on a Liouville-type result for a system of fourth-order equations in RN. <i>Electronic Journal of Differential Equations, 2002</i>(99), pp. 1-20.