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This paper presents rigorous proofs of the asymptotic solutions of a nonlinear ordinary equation, $\epsilon n f^(iv) = (f-2\epsilon) f''' - f' f''$ subject to boundary conditions:
$f(0) = 0, f(1) = 1, f'(1) = 0, lim_(n \to 0^+) sqrtn f''(n)=0.$