Bifurcation theory is used to prove the existence of positive solutions of some classes of semi-positone problems with nonlinear boundary conditions -u′′=λf(t,u),t∈(0,1),u(0)=0,u′(1)+c(u(1))u(1)=0,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} {\left\{ \begin{array}{ll} -u''=\lambda f(t, u), \qquad t\in (0,1),\\ u(0)=0, \quad u'(1)+c(u(1))u(1)=0,\\ \end{array}\right. } \end{aligned}$$\end{document}where c:[0,∞)→[0,∞)\documentclass[12pt]{minimal}
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\begin{document}$$c:[0, \infty )\rightarrow [0, \infty )$$\end{document} is continuous, f:[0,∞)→R\documentclass[12pt]{minimal}
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\begin{document}$$f:[0, \infty )\rightarrow \mathbb {R}$$\end{document} is continuous and f(t,0)<0\documentclass[12pt]{minimal}
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\begin{document}$$f(t,0)<0$$\end{document} for t∈[0,1]\documentclass[12pt]{minimal}
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\begin{document}$$t\in [0,1]$$\end{document}.
