Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.
A new approach to the calculation of the points at which the root locus crosses the imaginary axis is proposed and the corresponding parameters are given.Further,this method to analyze polynomial convexity is used.Examples are given for illustration.It is shown that this approach is simple and useful to determine the Hurwitz stable polynomial.
