Bifurcation method for solving multiple positive solutions to Henon equation on the unit cube

► Three algorithms based on the bifurcation method are applied to solving the D 4 ( 3 ) symmetric positive solutions to the boundary value problem of Henon equation. ► Taking r in Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation points are found via the extended systems o...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2011-09, Vol.16 (9), p.3673-3683
Main Authors: Li, Zhao-xiang, Zhu, Hai-long, Yang, Zhong-hua
Format: Article
Language:English
Subjects:
Algorithms
Bifurcations
Boundary value problems
Branch switching
Computer simulation
Extended system
Henon equation
Mathematical analysis
Mathematical models
Multiple solutions
Nonlinearity
Switching
Symmetry-breaking bifurcation
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Summary:► Three algorithms based on the bifurcation method are applied to solving the D 4 ( 3 ) symmetric positive solutions to the boundary value problem of Henon equation. ► Taking r in Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation points are found via the extended systems on the branch of the D 4 ( 3 ) symmetric positive solutions. ► Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction. Three algorithms based on the bifurcation method are applied to solving the D 4(3) symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation points are found via the extended systems on the branch of the D 4(3) symmetric positive solutions. Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov–Schmidt reduction.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2010.12.023