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Existence results of three-point boundary value problems for second-order ordinary differential equations. (English) Zbl 1208.34019

Summary: We establish existence results of the following three-point boundary value problem:
\[ u''(t)+f(t,u(t))=0, \quad t\in (0,1), \]
\[ u(0)=0 \quad\text{and}\quad u(1)=\delta u(\eta ), \]
where \(0<\eta <1\) and \(0<\delta \leq 1\). The approach applied in this paper is the upper and lower solution method associated with basic degree theory or Schauder’s fixed point theorem. The function \(f\) is Carathéodory or singular on its domain.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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References:

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