Numerical Methods for Computing Nonlinear Eigenpairs: Part I. Iso-Homogeneous Cases

With a Rayleigh quotient formulation, a local minimax method is developed to solve a class of (iso-homogeneous) nonlinear eigenpair problems for multiple solutions in Banach spaces following their instability order. The algorithm is implemented to compute (weighted) eigenpairs of the p-Laplacian. Numerical eigenfunctions are illustrated by their graphics. Several interesting phenomena have been observed and are open for further investigation. Mathematical analysis related to convergence and instability order of computed eigenfunctions, etc., are also presented.