We investigate the steady-state equations of motion of the generalized Newtonian fluid in a bounded domain Omega subset of R-N, when N = 2 or N = 3. Applying the tools of nonlinear analysis (Smale's theorem, theory of Fredholm operators, etc.), we show that if the dynamic stress tensor has the 2-structure then the solution set is finite and the solutions are C-1-functions of the external volume force f for generic f. We also derive a series of properties of related operators in the case of a more general p-structure, show that the solution set is compact if p > 3N/(N + 2) and explain why the same approach as in the case p = 2 cannot be applied if p not equal 2. (C) 2018 Elsevier Ltd. All rights reserved.