Depends on how you envision the structure of the giant size hair. A hair does not have a uniform composition, it consists of coaxial layers of different strength. So is reasonable to assume that surface forces contribute significantly to the strength of the hair.
Thus if you increase the size...
Thank you. Perhaps I should mention that I can find a solution using linearization and iteration. The physical origins is in a branch of fluid dynamics. Typically one assume only one solution. However I think that there should be several solutions, at least if |C| is small compared to |A| and |B|.
In my work I've encountered equations of the type:
(Ax).*(Bx) + Cx = d
Where A,B and C are non-unitary square matrices, x and d column vectors and .* denote component-wise multiplication.
I have a few books which discuss nonlinear matrix equations, but not of this kind. Any suggestions?