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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 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
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