Bifurcation method for solving multiple positive solutions to Henon equation

被引：12
|
作者：
Yang ZhongHua [1 ]
Li ZhaoXiang [1 ]
Zhu HaiLong [2 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] AnHui Univ Finance & Econ, Dept Math, Bangbu 233030, Peoples R China
来源：
SCIENCE IN CHINA SERIES A-MATHEMATICS | 2008年 / 51卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Henon equation; symmetry-breaking bifurcation; multiple solutions; extended system; branch switching; pseudo-arclength continuation; 35J65; 85A15;
D O I：
10.1007/s11425-007-0198-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Three algorithms based on the bifurcation method are applied to solving the D (4) symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bifurcation parameter, the D (4)-Delta (d) (D (4) - Delta(1), D (4) - Delta(2)) symmetry-breaking bifurcation points on the branch of the D (4) symmetric positive solutions are found via the extended systems. Finally, Delta (d) (Delta(1), Delta(2)) symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.
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页码：2330 / 2342
页数：13
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