Multiple solutions of a boundary layer problem

The laminar boundary layer flow on a continuous moving porous flat plate with suction or injection is governed by the nonlinear differential equationf‴(η)+f(η)f″(η)=0,f‴(η)+f(η)f″(η)=0,with boundary conditionsf(0)=-C,f′(0)=ξ,f′(+∞)=1,where η is the similarity variable, f(η) is related to the stream function, and C and ξ are constants. This paper presents a rigorous proof of the existence of multiple solutions to the boundary value problem by a shooting method on [0, ∞).