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

Abstract

Three algorithms based on the bifurcation theory are proposed to compute the 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 ) 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.