We are concerned with the third-order nonlinear equation f‴ + [(m + 1) / 2] f f″ - m f ′2 = 0 on (0, ∞), satisfying the boundary conditions f (0) = a ∈ R, f′ (0) = 1 and f′ (∞) = 0. The problem arises in the study of similarity solutions in two physically different contexts of fluid mechanics: free convection in a porous medium and flow adjacent to a stretching wall. We shall address two open questions: the first one is the uniqueness of bounded solutions for m ∈ (- 1 / 3, 0) and a < 0, and the second one is the structure of solutions for m ∈ (- 1 / 2, - 1 / 3) and a ≤ 0. Our results complement earlier results in the literature.
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