Bifurcation method for solving multiple positive solutions to Henon equation

被引：0
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作者：
ZhongHua Yang
ZhaoXiang Li
HaiLong Zhu
机构：
[1] Shanghai Normal University,Department of Mathematics
[2] AnHui University of Finance & Economics,Department of Mathematics
来源：
Science in China Series A: Mathematics | 2008年 / 51卷
关键词：
Henon equation; symmetry-breaking bifurcation; multiple solutions; extended system; branch switching; pseudo-arclength continuation; 35J65; 85A15;
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学科分类号：
摘要：
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 bifurcation 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) 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：12
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