Abstract: By using the fixed point theorem in cones, the author study the existence of multiple positive solutions for nonlinear third-order three-point boundary value problems where ρ>0 is a constant, 0<η<1, α>0, f: ［0,1］×［0,∞)→［0,∞) is a continuous function. The results show that when f satisfies certain conditions, there are countable multiple positive solutions for the problem.

Key words: nonlinear, third-order, fixed point theorem, multiple positive solutions, Green’s function