A Two-Parameter Shooting Problem for a Second-Order Differential Equation

We show that the set of global, positive solutions of the second order differential equation , for 1 < p < 2 is a one-parameter family (uλ)λ ≥0. For all λ ≥ 0, uλ behaves like (−t/p)1/(p−1) as t → − ∞. As t → + ∞, uλ behaves like t−1/(p−1) for all λ > 0, while u0 is the unique global solution that behaves like e−t2/4. These solutions arise in the calculation of a boundary layer for a convection-diffusion equation.