A two-point boundary value problem arising in boundary layer theory

A two-point boundary value problem of second order is restudied, which describes both a similarity boundary-layer flow induced by a moving permeable plane surface and a self-similar free convection boundary-layer flow over a vertical permeable flat plate embedded in a fluid-saturated porous medium. It is proved that there exists a λmin∈[1,2/3] such that this problem has a unique normal solution ϕ(η;λ)ϕ(η;λ) for all λ⩾λminλ⩾λmin and the solution ϕ(η;λ)ϕ(η;λ) is strictly decreasing with respect to both η⩾0η⩾0 and λ⩾λminλ⩾λmin; moreover, ϕ′(0;λmin)=0ϕ′(0;λmin)=0 and ϕ′(0;λ)ϕ′(0;λ), as a function of λ  , is strictly decreasing for λ⩾λminλ⩾λmin.