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On an \(m\)-point-boundary-value problem for second-order ordinary differential equations. (English) Zbl 0815.34012

An \(m\)-point boundary value problem of the form \(x'' = f(t,x,x')\), \(x(0) = 0\), \(x(1) = \sum^{m-2}_{i=1} a_ ix(\xi_ i)\) with \((t,x) \in [0,1] \times R\) is studied. Using the Leray-Schauder continuation theorem and the Wirtinger type inequality, the authors give conditions for the existence and uniqueness of a solution for this BVP. Theorems of the paper extend some recent results of the first author [J. Math. Anal. Appl. 186, 277-281 (1994; Zbl 0805.34017)].

MSC:

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

Citations:

Zbl 0805.34017
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References:

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