## 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

Zbl 0805.34017
Full Text:

### References:

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