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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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