On solutions of some singular, non-Linear differential equations arising in boundary layer theory

Abstract Solutions for a class of singular, non-linear, second-order differential equations arising in boundary layer theory with suction/injection, when Crocco variables are employed, are obtained. Existence, uniqueness, and analyticity results are established for boundary conditions corresponding to flow of a uniform stream past a semi-infinite flat plate (classical problem of Blasius) and for the flow behind weak expansion. Since the standardization technique (in Refs. [8, 9, 11]) does not work, a new technique is developed and used in proving existence and uniqueness theorems. Furthermore, the analytical solutions are compared with the numerical ones.