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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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