Computational methods for nonlinear elliptic eigenvalue problems

AbstractIn this paper, methods for finding nontrivial solutions of the nonlinear eigenvalue problem −δu = λF′(u) are considered. An equivalent variational formulation is used to obtain an iterative procedure for solving the problem with a general (non-convex) function F(u). The global convergence of this procedure is established, i.e., convergence from any initial guess. The method is applied to a test problem with F(u) = − cos u