Uniqueness implies existence and uniqueness conditions for a class of \((k+j)\)-point boundary value problems for \(n\)-th order differential equations (Q2888781)
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scientific article; zbMATH DE number 6042599
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniqueness implies existence and uniqueness conditions for a class of \((k+j)\)-point boundary value problems for \(n\)-th order differential equations |
scientific article; zbMATH DE number 6042599 |
Statements
4 June 2012
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boundary value problem
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uniqueness
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existence
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unique solvability
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nonlinear interpolation
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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)
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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 \(1\leq k\leq n-j\).
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