A numerical method for finding multiple co-existing solutions to nonlinear cooperative systems

DOI10.1016/J.APNUM.2007.09.007zbMath1158.65081OpenAlexW1965230540MaRDI QIDQ952807

Xudong Yao, Xianjin Chen, Jian Xin Zhou

Publication date: 14 November 2008

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2007.09.007

zbMATH Keywords

convergencecritical pointsmultiple solutionscoupled nonlinear Schrödinger equationsvector solitonscooperative elliptic systemsco-existing statesmin-orthogonal method

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational principles in infinite-dimensional spaces (58E30) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (10)

A local min-max-orthogonal method for finding multiple solutions to noncooperative elliptic systems ⋮ Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of semilinear elliptic Dirichlet problem involving concave and convex nonlinearities. I: Algorithms and convergence ⋮ A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems. I. Algorithm and global convergence ⋮ An improved local-min-orthogonal method for finding multiple solutions to nonlinear elliptic PDEs ⋮ Finding multiple solutions to elliptic systems with polynomial nonlinearity ⋮ Bifurcation method for solving multiple positive solutions to Henon equation on the unit cube ⋮ Estimate of Morse index of cooperative elliptic systems and its application to spatial vector solitons ⋮ A local min-orthogonal based numerical method for computing multiple coexisting solutions to cooperative \(p\)-Laplacian systems ⋮ Global Sequence Convergence of a Local Minimax Method for Finding Multiple Solutions in Banach Spaces ⋮ Convergence analysis of a minimax method for finding multiple solutions of semilinear elliptic equation.: I: On polyhedral domain

Cites Work

• A local min-orthogonal method for finding multiple saddle points.
• The existence of positive solution of elliptic system by a linking theorem on product space.
• On the Morse indices of sign changing solutions of nonlinear elliptic problems
• Existence results for the positive solutions of nonlinear elliptic systems
• Asymptotically linear cooperative elliptic system: existence and multiplicity
• Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates
• Minimax theorems
• Computing electronic structures: a new multiconfiguration approach for excited states
• Stability of Multihump Optical Solitons
• A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs
• Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers
• A high-linking algorithm for sign-changing solutions of semilinear elliptic equations
• A Local Minimax-Newton Method for Finding Multiple Saddle Points with Symmetries
• Instability analysis of saddle points by a local minimax method
• Convergence Results of a Local Minimax Method for Finding Multiple Critical Points
• A mountain pass method for the numerical solution of semilinear elliptic problems
• VORTICES IN MULTICOMPONENT BOSE–EINSTEIN CONDENSATES
• A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasi-linear Elliptic PDE
• An Efficient and Stable Method for Computing Multiple Saddle Points with Symmetries
• Multiple solutions for asymptotically linear elliptic systems

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