Bifurcation method for computing the multiple positive solutions to p-Henon equation

In this paper, we proposed the algorithms to solving the D4 symmetric positive solutions to the boundary value problem of p-Henon equation. Taking r in p-Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the D4 symmetric positive solutions is found via the extended systems. Based on the Liapunov-Schmidt reduction, other symmetric positive solutions are computed by the branch switching method.