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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 $f$.

##### MSC:
 34B18 Positive solutions of nonlinear boundary value problems for ODE 34B08 Parameter dependent boundary value problems for ODE 34B10 Nonlocal and multipoint boundary value problems for ODE 34B27 Green functions
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##### References:
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