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 D4(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 D4(3) symmetric positive solutions. Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov–Schmidt reduction.

Research highlights
► Three algorithms based on the bifurcation method are applied to solving the D4(3)D4(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 D4(3)D4(3) symmetric positive solutions.
► Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.