On the Existence of Similar Solutions of Some Boundary Layer Problems

Abstract

The first part deals with the continuity and monotonicity of functions of the parameters determining the range of existence of solutions of the Falkner–Skan equation considered by Iglisch and Kemnitz (and by Hartman). It also deals with the continuous and monotonic dependence on parameters of the maximal solution and its derivative. In the second part, we give existence theorems and physically significant properties for solutions of some problems associated with the names of Pohlhausen and Stewartson. Some of these problems have also been treated by Hastings. The method depends on Tikhonov’s fixed-point theorem and on the consideration of a boundary value problem for a nonlinear second order equation on $[0,\infty )$. Existence for this singular boundary value problem is obtained by Nagumo’s method of sub- and supersolutions, and uniqueness by properties of principal solutions of disconjugate linear second order equations. The third part is concerned with more general boundary value problems on $[0,\infty...