Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bifurcation parameter, the D4−Σd(D4 − Σ1, D4 − Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.
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