A 2-PARAMETER SHOOTING PROBLEM FOR A 2ND-ORDER DIFFERENTIAL-EQUATION

We show that the set of global, positive solutions of the second order differential equation [GRAPHICS] for 1 < p < 2 is a one-parameter fam ily (u(lambda))lambda greater-than-or-equal-to 0. For all lambda grate r-than-or-equal-to 0, u(lambda) behaves like (-t/p)1/(p-1) as t --> - infinity. As t --> + infinity, u(lambda) behaves like t-1/(p-1) for al l lambda > 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. (C) 1994 Academic Press, Inc.