Abstract We investigate positive solutions for three-component competition-diffusion systems within B₁ RN B 1 ⊂ R N: aligned\ array{ll - u₁= u₁ (1-u₁) - u₁ (u₂+ u₃), & in\ B₁, \\ - u₂= u₂ (1-u₂) - u₂ (u₁ + u₃), & in\ B₁, \\ - u₃= u₃ (1-u₃) - u₃ (u₁+u₂), & in\ B₁, \\ u₁ n= u₂ n= u₃ n=0, & on B₁, \\ array. aligned - Δ u 1 = μ u 1 (1 - u 1) - β u 1 (u 2 + u 3), in B 1, - Δ u 2 = μ u 2 (1 - u 2) - β u 2 (u 1 + u 3), in B 1, - Δ u 3
Li et al. (Fri,) studied this question.