Abstract: The author considered the existence and multiplicity of positive solutions of nonhomogeneous second-order three-point boundary value problems by using topological degree theory and the method of upper and lower solutions when the nonlinear term f satisfied superlinear growth conditions. The results show that there are  at least two positive solutions, one positive solution and no solution of the problem  when the parameter b is in  different value ranges.

Key words: three-point boundary value problem, multiplicity, upper and lower solutions, topological degree theory