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Positive solutions of a nonlinear three-point boundary-value problem. (English) Zbl 0926.34009
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:
34B15 Nonlinear boundary value problems for ordinary differential equations
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