  A multigrid method is proposed for solving nonlinear eigenvalue problems by
the finite element method. With this new scheme, solving nonlinear eigenvalue
problem is decomposed to a series of solutions of linear boundary value
problems on multilevel finite element spaces and a series of small scale
nonlinear eigenvalue problems. The computational work of this new scheme can
reach almost the same as the solution of the corresponding linear boundary
value problem. Therefore, this type of multilevel correction scheme improves
the overfull efficiency of the nonlinear eigenvalue problem solving.
