A Local Min-orthogonal Method For Finding Multiple Eigen-pairs Of Cooperative P-Laplacian Systems

The numerical computation for Eigenpair problem of the Cooperative p-Laplacian Systems is studied in this thesis. First of all, With a Rayleigh quotient formulation, the Eigenpair problem of the Cooperative p-Laplacian Systems is transformed into solv-ing the critical point of the Rayleigh-quotient functional. When the iso-homogeneous conditions are met, Solving the Eigenpair problem of the Cooperative p-Laplacian Sys-tems can be proved to be equivalent to finding the critical point of the corresponding Rayleigh-quotient functional. Then the definition of pseudo gradient and the L-_L se-lection function and the modified pseudo gradient are in turn introduced in the Banach space. In the Banach space, Pseudo gradient act as a search direction play a important role in algorithm. Modified pseudo gradient lemma ensure the projection of pseudo gradient,so as to make the iterative function points avoid degenerating to the old so-lution function space. Besides,The step size lemma and the characterization of the critical point or the saddle point are given in this article. On the basis of these theories, An improved Local Min-Orthogonal (LMO)algorithm applied in the Banach space is developed successfully in this paper. At the same time, the skills of pseudo gradient computation and the method for solving other important issues are studied in this pa-per. In addition, the convergence of the LMO algorithm is proved in this paper. Finally, some numerical example in different regions are given respectively, the numerical re-sults of which are good. The successful numerical calculation confirm the effectiveness of improvement method for finding multiple Eigen-pairs of p-Laplacian systems.