Bifurcation method for solving multiple positive solutions to Henon equation on the unit cube

Abstract

Three algorithms based on the bifurcation method are applied to solving the D 4(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 D 4(3) symmetric positive solutions. Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov–Schmidt reduction.