Nonuniqueness of solutions to differential equations for boundary-layer approximations in porous media

The free convection, along a vertical flat plate embedded in a porous medium, can be described in terms of solutions to f''' + alpha+1/2 f f" - alpha f'(2) = 0, for all t is an element of (0, +infinity). The purpose of this Note is to study the nonuniqueness of solutions to this problem, with the initial conditions, f (0) = a is an element of R and f'(0) is an element of {0, 1}, where alpha is an element of (-1/3, 0). No assumption at infinity is imposed. We show that this problem has an infinite number of unbounded global solutions. Moreover, we prove that the first and the second derivative of solutions tend to 0 as t approaches infinity.