Existence and unicity of solutions of n-point boundary value problems (Q755960)

The paper presents criteria for the existence and uniqueness of solutions to the n-point boundary value problem \(y^{(n)}=f(x,y,y',...,y^{(n- 1)}),\quad y(x_{\ell})=y_{\ell},\quad \ell =1,2,...,n,\) where f is continuous on a subset of \({\mathbb{R}}^ n\), \(y_ 1,...,y_{\ell}\in {\mathbb{R}}\) and \(x_ 1<x_ 2<...<x_ n\).