On the Asymptotic Behaviour of Solutions of a Differential Equation in Boundary Layer Theory

The asymptotic behavior, as t → ∞, of solutions of the singular boundary value problem u′′ + u u′ + λ (1 − u′ 2 ) = 0, u′ (0) = α, u′ (0) = β and u′ (∞) = 1, subject to 0 < u′(t) < 1 for 0 < t < ∞, is discussed. It is shown that if λ ≥ 0 and if the solution u exists, then (1). If λ < 0 and if a solution exists, then there is a unique one satisfying (1) while the other (if any) satisfy (2).