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...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.展开更多
In this paper, an algorithm is proposed to solve the 0（2） symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking 1 in the p- Henon equation as a bifurcation parameter, the symmetr...In this paper, an algorithm is proposed to solve the 0（2） symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking 1 in the p- 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. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10671130)the Science Foundation of Shanghai Municipal Education Commission (Grant No. 05DZ07)+2 种基金Shanghai Leading Academic Discipline Project (Grant No. T0401)Leading Foundation of Shanghai Science and Technology Commission (Grant No. 06JC14092)the Foundation of the Scientific Computing Key Laboratory of Shang-hai Universities
文摘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.
基金Project supported by the National Natural Science Foundation of China (No. 10901106)the Shanghai Leading Academic Discipline Project (No. S30405)+2 种基金the Shanghai Normal University Academic Project (No. SK200936)the Natural Science Foundation of Shanghai (No. 09ZR1423200)the Innovation Program of Shanghai Municipal Education Commission (No. 09YZ150)
文摘In this paper, an algorithm is proposed to solve the 0（2） symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking 1 in the p- 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. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.
