A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasi-linear Elliptic PDE
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A minimax method for finding multiple critical points in Banach spaces is developed by using a modified pseudogradient. The method is implemented successfully to solve several quasi-linear elliptic boundary value problems for multiple solutions. Numerical solutions are presented by their profiles to illustrate the theory and method. A unified convergence result of the algorithm is established in a subsequent paper [X. Yao and J. Zhou, A Unified Convergence Result on a Minimax Method for Finding Multiple Critical Points in Banach Spaces, preprint]. 2005 Society for Industrial and Applied Mathematics.
SIAM Journal on Scientific Computing
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Yao, Xudong||Zhou, Jianxin