Bifurcation method for solving multiple positive solutions to Henon equation on the unit cube

被引：2
|
作者：
Li, Zhao-xiang [1 ,2 ]
Zhu, Hai-long [3 ]
Yang, Zhong-hua [1 ,2 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Sci Comp Key Lab Shanghai Univ, Shanghai 200234, Peoples R China
[3] AnHui Univ Finance & Econ, Dept Math, Bangbu 233030, Peoples R China
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2011年 / 16卷 / 09期
基金：
上海市自然科学基金;
关键词：
Henon equation; Symmetry-breaking bifurcation; Multiple solutions; Extended system; Branch switching; ELLIPTIC-EQUATIONS; GROUND-STATES; ASYMPTOTIC PROFILE; SYSTEMS;
D O I：
10.1016/j.cnsns.2010.12.023
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(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 D-4(3) symmetric positive solutions. Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
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页码：3673 / 3683
页数：11
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