Abstract: By using the Krein-Rutman theorem and Dancer global bifurcation theory, the author studies the global structure of positive solutions for nonlinear third-order three-point boundary value problem, where r>0 is a parameter, 0<η<1, α,β>0, and the nonlinear term f∈C(［0,1］×［0,∞),［0,∞)) satisfies asymptotic linear growth condition at 0 and ∞.

Key words: multipoint boundary value problem, positive solution, global structure, bifurcation theorem