Abstract: This paper considers the global structure of the set of positive solutions of nonlinear third-order ordinary differential equations boundary value problems{-u⁽³⁾(t)=λf(t,u(t)), a.e. t∈［0,1］,u(0)=u'(0)=0, u'(1)=αu'(η),where f:［0,1］×R→［0,∞)is a L¹-Carathéodory function, 0<η<1, 1<α<1/η are given constants. When f satisfies the linear growth condition, the paper obtains the global structure of the set of positive solutions of the problem by using Rabinowitz global bifurcation theorem.

Key words: multipoint boundary value problem, principle eigenvalue, bifurcation, positive solution