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In this paper,we consider the vector nonlinear boundary value problem:εy<sup>v</sup>=f（x,y,z,y′,ε）,y（0）=A<sub>1</sub>,y（1）=B<sub>1</sub>εz<sup>v</sup>=g（x,y,z,z′,ε）,z（0）=A<sub>2</sub>,z（1）=B<s