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Uniqueness implies existence and uniqueness conditions for a class of \((k+j)\)-point boundary value problems for \(n\)-th order differential equations. (English) Zbl 1254.34029

The paper deals with uniqueness and existence of solutions for a class of multipoint boundary value problems for \(n\)-th order ordinary differential equations. The authors consider so-called \(\left( k;j\right) \)-point boundary conditions and prove that uniqueness of solutions of the \(\left( n-j_{0};j_{0}\right) \)-point BVP implies unique solvability of the \(\left( k;j\right) \)-point BVP, for all \(1\leq j\leq j_{0}\) and \(1\leq k\leq n-j\).

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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