A bifurcation method for solving multiple positive solutions to the boundary value problem of the Henon equation on a unit disk

Three algorithms based on the bifurcation theory are proposed to compute the O(2)O(2) symmetric positive solutions to the boundary value problem of the Henon equation on the unit disk. Taking l   in the Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O(2)O(2) symmetric positive solutions is found via the extended systems. Finally, other symmetric positive solutions are computed by the branch switching method based on the Lyapunov–Schmidt reduction.