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Zbl 0958.34019
Ma, Ruyun
Multiplicity of positive solutions for second-order three-point boundary value problems.
(English)
[J] Comput. Math. Appl. 40, No.2-3, 193-204 (2000). ISSN 0898-1221

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 $f$.
[Nataliya Bantsur (Ky{\" i}v)]
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B08 Multi-parameter boundary value problems
34B10 Multipoint boundary value problems
34B27 Green functions

Keywords: three-point boundary value problem; positive solution; cone; fixed-point index

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