| 摘 要： | We study the boundary value problem where ε, μ are two positive parameters, are n-dimensional vector functions and the boundary is perturbed. This vector boundary problem does not appear to have been studied. Under appropriate assumptions we obtain existence of solution and satisfies where i=1, 2, …, n; Here y_(0,0)~t(t) is a solution of reduced equation f~i (t, y~1, …, y_(0,0)~t,…, y~n, 0, 0)=0, while y_(s-k,k)~i(t) (k=0, 1,…, s; s=1, 2, …, m) can be obtained successively from certain linear systems.
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