Nonuniqueness results for quasilinear elliptic systems

In this note we would like to consider systems of the type 1 https://www.w3.org/1998/Math/MathML"> { - ( a i ( u 1 , …   , u n ) u i ′ ) ′ = f i ⁢     i n ⁢     I = ( a , b ) ∀ i = 1 , 2 , . , n , u i ∈ H 1 ( ( a , b ) ) ∀ i = 1 , 2 , . , n , u i ( a ) = A i ⁢       e t ⁢       u i ( b ) = B 1 ⁢   ∀ i = 1 , 2 , . , n , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/math1a.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where f_i are in H ^-1((a, b)) and a_i are continuous functions verifying for some constants α, β 2 https://www.w3.org/1998/Math/MathML"> 0 < α ≤ a i ≤ β ∀ i = 1 , ... , n . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062271/3a9a5b62-3a88-4cc5-923a-97624426ebfd/content/math2a.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> We will set u = (u ₁····u_n ).