摘要:We establish the existence of a nontrivial solution of system: −∆ p u = λ a(x)u|u| p−2 + λ 0 c(x)u|u| α−1 |v| β+1 + f in Ω −∆ q v = µ b(x)v|v| q−2 + λ 0 c(x)|u| α+1 v|v| β−1 + g in Ω (u,v) ∈ W 1,p 0 (Ω) × W 1,q 0 (Ω) under some restrictions on λ,µ,λ 0 ,α,β,f and g. We show this result by a local minimization.