Abstract We study positive radial solutions to n × n nonlinear elliptic systems of the form: { − Δ u i = λ K i ( | x | ) f i ( u i + 1 ) in x ∈ Ω E , u i = 0 on | x | = r 0 , u i → 0 as | x | → ∞ , where i ∈ { 1 , 2 , … , n } , u 1 ≡ u n + 1 , Δ u : = div ( ∇ u ) , λ > 0 , N > 2 , r 0 > 0 , Ω E : = { x ∈ R N | | x | > r 0 } , K i ∈ C ( ( r 0 , ∞ ) , ( 0 , ∞ ) ) and f i ∈ C ( [ 0 , ∞ ) , R ) . We establish existence, multiplicity and uniqueness results for various nonlinearities f i .

中文翻译：

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球外部非线性椭圆系统类的正径向解

摘要 我们研究了以下形式的 n × n 非线性椭圆系统的正径向解： { − Δ ui = λ K i ( | x | ) fi ( ui + 1 ) in x ∈ Ω E , ui = 0 on | × | = r 0 , ui → 0 as | × | → ∞ , 其中 i ∈ { 1 , 2 , … , n } , u 1 ≡ un + 1 , Δ u := div ( ∇ u ) , λ > 0 , N > 2 , r 0 > 0 , Ω E : = { x ∈ RN | | × | > r 0 }，K i ∈ C (( r 0 , ∞ ) , ( 0 , ∞ ) ) 和fi ∈ C ( [ 0 , ∞ ) , R ) 。我们为各种非线性 fi 建立存在性、多重性和唯一性结果。