Abstract
The existence of positive solution is obtained for the following nonlinearthree-point boundary value problem\begin{equation*}\left\{\begin{array}{l}u^{\prime \prime }(t)+a(t)f(u(t))=0,\quad t\in (0,1) \\[12pt]\beta u(0)-\gamma u^{\prime }(0)=0,\quad u(1)=\alpha u(\eta ),%\end{array}%\right.\end{equation*}%where $$\beta ,\gamma \geq 0,0 0.$$
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