## Solvability of three point boundary value problems for second order differential equations with deviating arguments.(English)Zbl 1154.34367

Summary: The monotone iterative technique is used to boundary problems for second order ordinary differential equations with deviating arguments $x''(t)=f(t,x(t),x(\alpha(t))),\quad t\in[0,T],$
$x(0)=0, x(T)=rx(\gamma),$ where the numbers $$\gamma,T,r$$ are fixed with $$0<\gamma<T$$. The cases of positive and negative $$r$$ are considered separately. Corresponding results are formulated when the problem has extremal solutions or weakly coupled extremal quasi-solutions.

### MSC:

 34K10 Boundary value problems for functional-differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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### References:

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