求解正六边形上Henon方程边值问题的分歧方法  

Bifurcation method for solving boundary value problems of nonlinear elliptic PDE′s in the area of Hexagon

作　　者：李红群[1] 郭谦[1] 李昭祥[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《纺织高校基础科学学报》2010年第3期259-262,共4页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(10901106);上海市自然科学基金资助项目(09ZR1423200);上海市教委创新项目(09YZ150);上海师范大学科研项目(SK200936)

摘　　要：用对称破缺分歧方法计算了非线性Henon方程边值问题在正六边形区域上的多个非平凡解.讨论了解的各种对称性质,画出了从各个分歧点出发的具有各种对称性质的解枝图,从而可以直观的看出解的性态.The theory and algorithm of symmetry-breaking bifurcation are applied to finding multiple solutions for boundary value problems of Henon equation in the area of Hexagon,different symmetry properties of nontrivial solutions were studied,and numerical multiple solutions which have vary symmetry properties bifurcating from bifurcation points are visualized,so the characteristic of solution can be seen intuitively.

关 键 词：HENON方程 多解 对称破缺 分歧 Liapunov-Schmidt方法 

分 类 号：O175[理学—数学]