本文研究了具有凸-凹-凸非线性项的狄利克雷边值问题正解的分支曲线。通过时间映射分析法，证明了在非线性项为渐近次线性时，边值问题的正解分支曲线为S-型曲线，从而确定了边值问题的正解的确切个数。 In this paper we study the bifurcation curve of the Dirichlet boundary value problem with convex- concave-convex nonlinearities. By using Time-map techniques, we prove that the bifurcation curve of the boundary value problem is S-shaped when the nonlinearities are asymptotic sublinear. Consequently, the exact multiplicity of positive solutions is determined.