Ljusternik–Schnirelman Minimax Algorithms and an Application for Finding Multiple Negative Energy Solutions of Semilinear Elliptic Dirichlet Problem Involving Concave and Convex Nonlinearities: Part I. Algorithms and Convergence

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• 作者：Xudong Yao
• 关键词：Ljusternik–Schnirelman critical point theory ; Ljusternik–Schnirelman minimax algorithm ; Semilinear elliptic equation ; Concave and convex nonlinearities ; Finite element method ; Convergence ; 58E05 ; 58E30 ; 35J91 ; 65N12 ; 65N30
• 刊名：Journal of Scientific Computing
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：66
• 期：1
• 页码：19-40
• 全文大小：1,381 KB
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• 作者单位：Xudong Yao (1)
  
  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691

文摘

In this paper, two minimax algorithms for capturing multiple saddle points are developed from well-known Ljusternik–Schnirelman critical point theory. Mathematical justification for these algorithms is established. Numerical experiment is carried out to calculate multiple negative energy solutions of semilinear elliptic Dirichlet problem involving concave and convex nonlinearities. Global sequence convergence result is verified. Keywords Ljusternik–Schnirelman critical point theory Ljusternik–Schnirelman minimax algorithm Semilinear elliptic equation Concave and convex nonlinearities Finite element method Convergence