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For given $${a \in \mathbb {R}}$$ , c f  b  of the differential equation f ′′′ + ff ′′ + g(f ′) = 0 satisfying the initial conditions f(0) = a, f ′ (0) = b, f ′′ (0) = c, where g is some nonnegative subquadratic locally Lipschitz function. It is proven that there exists b * > 0 such that f  b  exists on [0, + ∞) and is such that $${f'_b(t) \to 0}$$ as t → + ∞, if and only if b ≥ b *. This allows to answer questions about existence, uniqueness and boundedness of solutions to a boundary value problem arising in fluid mechanics, and especially in boundary layer theory.

On the solutions of a boundary value problem arising in free convection with prescribed heat flux