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In this paper, we investigate the solvability of n th-order Lipschitz equations y(n)=f(x,y,y′,…,y(n−1))Open image in new window, x1≤x≤x3Open image in new window, with nonlinear three-point boundary conditions of the form k(y(x2),y′(x2),…,y(n−1)(x2);y(x1),y′(x1),…,y(n−1)(x1))=0Open image in new window, gi(y(i)(x2),y(i+1)(x2),…,y(n−1)(x2))=0Open image in new window, i=0,1,…,n−3Open image in new window, h(y(x2),y′(x2),…,y(n−1)(x2);y(x3),y′(x3),…,y(n−1)(x3))=0Open image in new window, where n≥3Open image in new window, x1<x2<x3Open image in new window. By using the matching technique together with set-valued function theory, the existence and uniqueness of solutions for the problems are obtained. Meanwhile, as an application of our results, an example is given.

Solvability of n th-order Lipschitz equations with nonlinear three-point boundary conditions