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.

引用

页码：2330 / 2342

页数：13

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