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 λ min ∈ [ 1 , 2 / 3 ] such that this problem has a unique normal solution ϕ ( η ; λ ) for all λ ⩾ λ min and the solution ϕ ( η ; λ ) is strictly decreasing with respect to both η ⩾ 0 and λ ⩾ λ min ; moreover, ϕ ′ ( 0 ; λ min ) = 0 and ϕ ′ ( 0 ; λ ) , as a function of λ, is strictly decreasing for λ ⩾ λ min .