  In this paper we are concerned with the solutions of the differential
equation $f'''+ff''+g(f')=0$ on $[0,\infty)$, satisfying the boundary
conditions $f(0)=\alpha$, $f'(0)=\beta\geq 0$, $f'(\infty)=\l$, and where $g$
is some given continuous function. This general boundary value problem includes
the Falkner-Skan case, and can be applied, for example, to free or mixed
convection in porous medium, or flow adjacent to stretching walls in the
context of boundary layer approximation. Under some assumptions on the function
$g$, we prove existence and uniqueness of a concave or a convex solution. We
also give some results about nonexistence and asymptotic behaviour of the
solution.

Classical Analysis and ODEs