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Zbl 0926.34009
Ma, Ruyun
Positive solutions of a nonlinear three-point boundary-value problem. (English)
[J] Electron. J. Differ. Equ. 1999, Paper No.34, 8 p. (1999). ISSN 1072-6691/e

Summary: The author studies the existence of positive solutions to the boundary value problem $$ u''+a(t)f(u)=0,\quad t\in (0,1), \qquad u(0)=0,\quad\alpha u(\eta)=u(1) ,$$ with $0<\eta<1$ and $0<\alpha<1/\eta$. He shows the existence of at least one positive solution if $f$ is either superlinear or sublinear by applying a fixed point theorem in cones.

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE

Keywords: second-order multi-point boundary value problems; cone; fixed point

Cited in: Zbl 1101.34008 Zbl 1033.34030 Zbl 1032.34013 Zbl 0989.34009 Zbl 0964.34022

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