Bifurcation behavior of laminar flows of a boundary layer problem

This paper presents a theoretical analysis on the bifurcation behavior of solutions to a nonlinear equation f? ? ff″ = 0 with boundary conditions: f(0) = C, f′(0) = ξ and f′(∞) = 1 where ξ and C are parameters. It shows that if ξ ≥ 0 including the case ξ ≥ 1, then for any C the boundary value problem has at most one solution. However, for any ξ < 0, there exist some C < 0 such that the boundary value problem admits at least two solutions.