A class of two-point boundary value problems for systems of ordinary differential equations (Q1070405)

The paper deals with the two-point boundary value problems: \(x'=f(t,x)\), \(x^ 1(t_ 1)=a^ i\), \(i\in N\), \(x^ j(t_ 2)=b^ j\), \(j\in M\), where \(f:[t_ 1,t_ 2]\times {\mathbb{R}}^ n\to {\mathbb{R}}^ n\) and M and N are arbitrary subsets of \(\{\) 1,...,n\(\}\) such that card \(M+card N=n\). In particular, existence and uniqueness results are given, extending previous work.