Science in China Series A: Mathematics

, Volume 51, Issue 12, pp 2330–2342 | Cite as

Bifurcation method for solving multiple positive solutions to Henon equation

  • ZhongHua Yang
  • ZhaoXiang LiEmail author
  • HaiLong Zhu


Three algorithms based on the bifurcation method are applied to solving the D 4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bifurcation parameter, the D 4−Σ d (D 4 − Σ1, D 4 − Σ2) symmetry-breaking bifurcation points on the branch of the D 4 symmetric positive solutions are found via the extended systems. Finally, Σ d 1, Σ2) symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.


Henon equation symmetry-breaking bifurcation multiple solutions extended system branch switching pseudo-arclength continuation 


35J65 85A15 


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© Science in China Press and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiChina
  2. 2.Department of MathematicsAnHui University of Finance & EconomicsBangbuChina

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