We investigate the similarity solutions of a magnetohydrodynamics (MHD) boundary layer
problem arising in the two-dimensional steady boundary layer system for an incompressible
electrically conducting power-law fluid in the presence of magnetic and electric fields.
In the self-similar case, the boundary layer system is converted into a third-order
nonlinear differential equation depending on two parameters. When one of the two parameters
is negative, the existence and uniqueness of normal convex solutions and generalized
convex solutions to the boundary layer problem are established by the aid of the Helly
selection theorem. The asymptotic behavior of normal convex solutions at infinity
is also obtained. (C) 2019 Elsevier Ltd. All rights reserved.