Exact self-similar solutions of the magnetohydrodynamic boundary layer system for power-law fluids

In a particular self-similar case, the magnetohydrodynamic boundary layer system for an electrically conducting power-law fluid together with certain boundary conditions can be transformed into a boundary value problem for a third-order nonlinear ordinary differential equation, only whose (generalized) normal solutions possess the physical meaning of the original problem. Uniqueness, existence and nonexistence results are established for the problem. Representations are also given for all (generalized) normal solutions.