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**Multiplicity of positive solutions for second-order three-point boundary value problems.**
*(English)*
Zbl 0958.34019

The author studies the second-order three-point boundary value problem
\[
u''+\lambda h(t)f(u) = 0, \qquad t\in (0, 1), \tag{1}
\]

\[ u(0) = 0, \qquad \lambda u(\eta) = u(1), \tag{2} \] with \(\eta : 0 < \eta <1, 0 < \alpha < 1 / \eta .\) The author studies the multiplicity of positive solutions to (1), (2) using the method of upper and lower solutions, the Leray-Schauder degree theory and fixed-point index theorems. Notice, that the main theorem is proved using traditional methods of functional analysis with any monotonicity on \(f\).

\[ u(0) = 0, \qquad \lambda u(\eta) = u(1), \tag{2} \] with \(\eta : 0 < \eta <1, 0 < \alpha < 1 / \eta .\) The author studies the multiplicity of positive solutions to (1), (2) using the method of upper and lower solutions, the Leray-Schauder degree theory and fixed-point index theorems. Notice, that the main theorem is proved using traditional methods of functional analysis with any monotonicity on \(f\).

Reviewer: Nataliya Bantsur (Kyïv)

### MSC:

34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |

34B08 | Parameter dependent boundary value problems for ordinary differential equations |

34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |

34B27 | Green’s functions for ordinary differential equations |

Full Text:
DOI

### References:

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