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

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In this paper, we give existence and uniqueness results for solutions of nonlocal boundaryvector value problems of the form x ( 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 [ d g ( s ) ] x ( n − 1 ) ( s ) , where n2, ƒ : [0, 1] x ( R N 1 ) n → R N 1 is a Carathéodory function, g : [0, l] → R N 1 × R N 1 is a Lebesgue measurable N 1 × 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.