Existence and uniqueness of solutionsfor nonlocal boundary vector value problems of ordinary differential systems with higher order

In this paper, we give existence and uniqueness results for solutions of nonlocal boundaryvector value problems of the formx^(^n^)(t)=f(t,x(t),x^'(t),...,x^(^n^-^1^)(t)),t@?[0,1],x(0)=x^'(0)=...=x^(^n^-^2^)(0)=0,x^(^n^-^1^)(1)=@!"0^1[dg(s)]x^(^n^-^1^)(s), where n2, @? : [0, 1] x (R^N^"^1)^n -> R^N^"^1 is a Caratheodory function, g : [0, l] -> R^N^"^1 x R^N^"^1 is a Lebesgue measurable N"1 x N"1-matrix function and it satisfies g(0) = 0, the integral is in sense of Riemann-Stieltjes. The existence of a solutions is proven by the coincidence degree theory. As an application, we also give one example to demonstrate our results.