The objective of the present paper is to provide a detailed account of a local min-orthogonal method for finding multiple coexisting solutions to cooperative p-Laplacian systems. A local L-⊥ selection mapping on a product space of two Banach spaces is introduced in order to develop a local characterization of the coexisting solutions. Using this local characterization we propose a numerical algorithm for finding multiple coexisting solutions to the system and provide a subsequence convergence result of the algorithm. We also discuss the discretization of the problem using the finite element method and the associated convergence results of the numerical solutions. Finally, we provide the numerical results to demonstrate the efficiency of the proposed method and also to confirm its related theoretical results.

本文的目的是详细介绍一种局部最小正交方法，用于寻找协作p-拉普拉斯系统的多个共存解。本地L-⊥ 在两个 Banach 空间的乘积空间上的选择映射被引入以开发共存解的局部特征。使用这种局部特征，我们提出了一种数值算法，用于寻找系统的多个共存解，并提供算法的子序列收敛结果。我们还讨论了使用有限元方法对问题进行离散化以及相关的数值解的收敛结果。最后，我们提供了数值结果来证明所提出方法的有效性，并证实了其相关的理论结果。