Abstract
In this paper, we study the following elliptic system − Δ u = μ 1 u 3 + β u v 2 , x ∈ Ω − Δ v = μ 2 v 3 + β u 2 v , x ∈ Ω u , v > 0 , x ∈ Ω , u = v = 0 , x ∈ ∂ Ω , where Ω ⊂ R 4 is an annulus, μ 1 , μ 2 > 0 and β > 0 . By variational method, we prove that the system has a non-radial solution.
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