Bifurcation method for solving multiple positive solutions to Henon equation

Abstract

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 (Σ1, Σ2) symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.