## Method of successive approximations for a certain non-linear third order boundary value problem.(English)Zbl 0707.34019

A method of successive approximations formed by means of lower and upper solutions is applied to a monotone operator based on Green’s functions and used to investigate a boundary value problem of the form $x'''=f(t,x,x'),\quad \alpha_ 2x'(a_ 1)-\alpha_ 3x''(a_ 1)=A_ 1,\quad x(a_ 2)=A_ 2,\quad \gamma_ 2x'(a_ 3)+\gamma_ 3x''(a_ 3)=A_ 3,$ under suitable sign restrictions upon the $$\alpha_ i$$, the condition $$a_ 1<a_ 2<a_ 3$$ and some monotonicity conditions upon f.
Reviewer: J.Mawhin

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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### References:

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