Abstract: By using the principle of time maps, we study the exact multiplicity and bifurcation diagrams of positive solutions of Dirichlet problem for a prescried mean curvature equation in the onedimensional Minkowski space, where λ>0 and L>0 are parameters. We obtain the results that the above problem has no positive solution, exactly one positive solution and exactly two positive solutions when the nonlinear terms f(u)=u(e^u-1) and f(u)=e^u-1, respectively.

Key words: Minkowski space, mean curvature, time maps, exact multiplicity of positive solution, Dirichlet problem