Abstract
A rigorous mathematical analysis is given for a well-known problem for a third-order nonlinear ordinary differential equation, which arises in boundary layer theory in fluid mechanics and was firstly deduced by Falkner and Skan in 1930. It is proved that the problem is equivalent to a singular nonlinear two-point boundary value problem of second order. For the singular nonlinear boundary value problem, uniqueness, existence and nonexistence of positive solutions are established by utilizing a priori estimates, comparison principles and a modified shooting type method. These results are easily turned over to the original problem.
