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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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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Xudong Yao

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  1. Xudong Yao
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Yao, X. 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. J Sci Comput 66, 19–40 (2016). https://doi.org/10.1007/s10915-015-0010-y

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  • DOI: https://doi.org/10.1007/s10915-015-0010-y

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