The equation considered is \[ fⁱᵛ + R( {ff''' - f'f''} ) = 0,\] with boundary conditions \[ f(0) = f''(0) = 0, f(1) = 1, f'(1) = 0.\] It is shown that for all R there is at least one solution, and for sufficiently large R there are at least three solutions. The asymptotic behavior as R → - ∞ is also studied. This equation arises in studying laminar flow in a porous channel.
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Hastings et al. (1992) studied this question.
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