A note on the structure of similarity solutions arising in boundary layer flows

We consider a general boundary layer equation f ‴ + f f ″ − β f ′ 2 = 0 with the boundary condition f ( 0 ) = a , f ′ ( 0 ) = 1 , f ′ ( ∞ ) ≔ lim t → ∞ f ′ ( t ) = 0 , where β is a real constant. In this work, the structure of solutions for the case β ≥ 2 is studied. Combining with the previous results in the literature, the structure of solutions of the given problem can be determined completely.