Bifurcation of the positive solutions to Henon equation

Three algorithms based on the bifurcation method is 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 – ∑ d ( D 4 – ∑ 1 , D 4 – ∑ 2 ) symmetry‐breaking bifurcation point on the branch of the D 4 symmetric positive solutions is found via the extended systems. Finally, ∑ d (∑ 1 , ∑ 2 ) symmetric positive solutions = are computed by the branch switching method based on the Liapunov‐Schmidt reduction. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)