计算立方体上Henon方程多个正解的分歧方法

COMPUTING MULTIPLE SOLUTIONS TO THE BOUNDARY VALUE PROBLEM OF HENON EQUATION

本文首先应用分歧方法给出计算立方体上Henon方程边值问题D_4(3)对称正解的三种算法,然后以Henon方程中的参数r为分歧参数,在D_4(3)对称正解解枝上用扩张系统方法求出对称破缺分歧点,进而用解枝转接方法计算出其它具有不同对称性质的正解.

Three algorithms based on the bifurcation method are applied to computing the D4（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 D4（3） symmetric positive solutions. Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.